Q:

# How do you use the quadratic formula?

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### Quick Answer

The quadratic formula is ax2 + bx + c = 0. To solve for x, you must get it on one side: x = [ -b ± sqrt(b2 - 4ac) ] / 2a. Start by filling in all of the known variables. Calculate the answer.

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### Full Answer

1. Write down the equation

Write down the equation and the problem being solved. ax2 + bx + c = 0 x = [ -b ± sqrt(b2 - 4ac) ] / 2a for the problem x2 + 3x - 9 = 0

2. Fill in known variables

The next step is filling in all of the known variables, which are a, b and c. The variables a, b and c are the coefficients of each respective term. In the example x2 + 3x - 9 = 0, a equals 1, b equals 3, and c equals -9. In quadratic form, that looks like: x = [ -3 ± sqrt(32 - 4(1)(-9)] / 2(1).

3. Start solving

Use the order of operations: parentheses, exponents, multiplication, division, addition and subtraction (PEMDAS) to start solving the problem. These operations must be used in the specified order. Start with the parentheses first and complete all the operations within the parentheses/brackets.

x = [ -3 ± sqrt(32 - 4(1)(-9)] / 2(1)
x = [ -3 ± sqrt(9 - 4(-9)] / 2(1)
x = [ -3 ± sqrt(9 + 36)] / 2(1)
x = [ -3 ± sqrt(45)] / 2(1)
x = [ -3 ± 6.7] / 2(1)
x = 3.7 / 2(1) AND x = 9.7 / 2(1)

Then, use PEMDAS for the rest of the equation outside the parentheses.

x = 3.7 / 2 AND x = -9.7 / 2
x = 1.85 AND x = -4.85

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