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# Quadratic equation in one variable

- Example:
- Use the factoring method to solve this equation x
^{2}- 2x = 15

- Solution:
- The standard form of the quadratic equation is ax
^{2}+ bx + c = 0, in which a, b, c are constants with the coefficient a is not zero.

- Step 1:
- Write the given quadratic equation in standard form x
^{2}- 2x - 15 = 0 - Step 2:
- Factoring the expression on the left side of the equation.
- The figure above tell us that:
- First term: (x)(x) = x
^{2} - Middle term: (-5)(x) + (3)(x) = -5x + 3x = - 2x
- Last term: (-5)(3) = -15
- Step 3:
- Solve ( x - 5 ) ( x + 3 ) = 0
- Use the zero property to set each factor equal to zero
- Step 4:
- Check if the solutions satisfy the original equation
- For x = 5, left side of the original equation = 5
^{2}- 2(5) = 25 - 10 = 15 = right side of the original equation, so it is solution. - For x = -3, left side of the original equation = (-3)
^{2}-2(-3) = 9 + 6 = 15 = right side of the original equation, so it is solution.

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