Quadratic equation in one variable

Example:
Use the factoring method to solve this equation x2 - 2x = 15
Solution:
The standard form of the quadratic equation is ax2 + 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 x2 - 2x - 15 = 0
Step 2:
Factoring the expression on the left side of the equation.
factoring polynomial example1
The figure above tell us that:
First term: (x)(x) = x2
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
solving quadratic equations
Step 4:
Check if the solutions satisfy the original equation
For x = 5, left side of the original equation = 52 - 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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