Q&A for How to Solve Quadratic Equations Using the Quadratic Formula

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Solve by the formula method: 2x^2 + x - 300 = 0.

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a = 2, b = 1, and c = -300. By the quadratic formula x = {-1 +/- √[1² - (4)(2)(-300)]} / (2)(2) = [-1 +/-√(1 + 2400)] / 4 = (-1 +/- √2401) / 4 = (-1 +/- 49) / 4 = 48/4 or -50/4 = 12 or -12½ = x. As odd as that second value seems, both of those x values do work in the original equation.

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What if my b is a negative?

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Community Answer

If b is negative, in the quadratic formula it becomes -(-b), or +b, meaning you're working with a positive b.

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How do you use completing a square?

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See Complete the Square , Solve Quadratic Equations and Factor Algebraic Equations .

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Do I have to leave it in the form of plus-minus, or can I make the plus equation separate from the minus one?

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It's your choice, but it's not mandatory to keep it in the plus-minus form. Most teachers and textbooks teach plus-minus, but that all depends on the material taught.

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What if b ITSELF is negative?

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When an already negative number has another negative sign in front of it, the negative number becomes positive. -(-b) = +b. So in the quadratic formula, the -b in front becomes b.

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