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How to Solve a Quadratic Equation When It Won’t Factor

When asked to solve a quadratic equation that you just can’t seem to factor (or that just doesn’t factor), you have to employ other ways of solving the equation, such as by using the quadratic formula. The quadratic formula is the formula used to solve for the variable in a quadratic equation in standard form.

Given a quadratic equation in standard form ax2 + bx + c = 0,

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Before you apply the formula, it’s a good idea to rewrite the equation in standard form (if it isn’t already) and figure out the a, b, and c values.

For example, to solve x2 – 3x + 1 = 0, you first say that a = 1, b = –3, and c = 1. The a, b, and c terms simply plug into the formula to give you the values for x:

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Simplify this formula one time to get

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Simplify further to get your final answer, which is two x values (the x-intercepts):

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