{"id":37500,"date":"2026-01-03T07:53:35","date_gmt":"2026-01-03T07:53:35","guid":{"rendered":"https:\/\/mp.moonpreneur.com\/math-corner\/?p=37500"},"modified":"2026-03-30T13:32:19","modified_gmt":"2026-03-30T13:32:19","slug":"sat-quadratics-tricks","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/sat-quadratics-tricks\/","title":{"rendered":"The Ultimate Guide to Solving SAT Quadratics in Seconds"},"content":{"rendered":"\t\t
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We\u2019ve all been there: the clock is ticking during the SAT, and you\u2019re staring at a quadratic equation that looks like it\u2019s going to take a full minute to factorise. When every second counts, you need more than just the “standard” way of doing things. In this blog, you are going to find the steps where you can just solve it in seconds. Yes! 2-3 seconds.<\/span><\/p>

Level 1: The “Reverse the Sign” Trick<\/strong><\/span><\/h3>

When you have a simple quadratic equation where the coefficient of x<\/span>\u00b2<\/span> \u00a0<\/span>is 1 (like\u00a0<\/span>x\u00b2<\/em><\/span>\u00a0\u221214<\/span>x<\/span><\/i>+48=0<\/span>), most students start writing out multiple lines of factorisation.<\/span><\/p>

The faster way:<\/b><\/span><\/h5>
  1. Find your factors:<\/b> Find two numbers that multiply to the last number (48) and add up to the middle number (-14). In this case, those numbers are -6 and -8.<\/span><\/li>
  2. Reverse the signs:<\/b> Simply flip the signs of those two numbers. Your solutions are <\/span>6 and 8<\/b>.<\/span><\/li><\/ol>

    It\u2019s that simple. Instead of writing out <\/span>(<\/span>x<\/span><\/i>\u22126)(<\/span>x<\/span><\/i>\u22128)=0<\/span>, you just find the factors and jump straight to the answer.<\/span><\/p>

    Recommended Reading<\/strong>: SAT Passport to Advanced Math Guide<\/a><\/p>

    Level 2: The “Transfer and Divide” Trick<\/strong><\/span><\/h3>

    Things get tricky when <\/span>x<\/span><\/i>\u00b2<\/span><\/i> has a coefficient greater than 1, such as <\/span>4<\/span>x\u00b2<\/span><\/i>\u00a0<\/span>\u2212<\/span>x<\/span><\/i>\u22123=0<\/span>. But we have something even better for these types of cases.<\/span><\/p>

    The faster way:<\/b><\/span><\/h5>
    1. Multiply <\/b>a<\/span><\/i> and <\/b>c<\/span><\/i>:<\/b> Take the first number (4) and multiply it by the last number (-3). Now, imagine a new equation: <\/span>x\u00b2 \u2212 x \u2212 12 = 0.<\/span><\/i><\/li>
    2. Find the factors for the new equation:<\/b> What multiplies to -12 and adds to -1? That would be -4 and +3.<\/span><\/li>
    3. Reverse the signs:<\/b> This gives you +4 and -3.<\/span><\/li>
    4. The Final Step (Don’t forget!):<\/b> Divide those numbers by the original first number (4). Your solutions are <\/span>4\/4 (which is 1) and -3\/4<\/b>.<\/span><\/li><\/ol>

      This method allows you to handle complex-looking problems mentally, saving you precious space on your scratch paper.<\/span><\/p>

      For a more detailed walkthrough, you can watch this video: <\/strong><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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      <\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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      Recommended Reading: <\/b>An overview of the SAT Math Test Sections<\/b><\/a><\/p>

      Why Does This Work?<\/b><\/span><\/h3>

      It might feel like a “hack”, but there is real math behind it. This shortcut is actually a <\/span>transformation of the <\/b>quadratic formula<\/b><\/a>. By shifting the coefficients, you create a temporary equation that is easier to solve, and then you “translate” the answer back to the original by dividing.<\/span><\/p>

      When to Use “Plan B”<\/b><\/p>

      As helpful as these tricks are, they rely on the equation being factorable. If you find yourself struggling to find the right factors after a few seconds, don’t panic. The sources recommend jumping straight to the <\/span>quadratic formula<\/b> as your reliable backup to ensure you get the right answer.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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      Cheat Guide to remember<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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