(x-3)(x+2)=56

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Solution for (x-3)(x+2)=56 equation:


Simplifying
(x + -3)(x + 2) = 56

Reorder the terms:
(-3 + x)(x + 2) = 56

Reorder the terms:
(-3 + x)(2 + x) = 56

Multiply (-3 + x) * (2 + x)
(-3(2 + x) + x(2 + x)) = 56
((2 * -3 + x * -3) + x(2 + x)) = 56
((-6 + -3x) + x(2 + x)) = 56
(-6 + -3x + (2 * x + x * x)) = 56
(-6 + -3x + (2x + x2)) = 56

Combine like terms: -3x + 2x = -1x
(-6 + -1x + x2) = 56

Solving
-6 + -1x + x2 = 56

Solving for variable 'x'.

Reorder the terms:
-6 + -56 + -1x + x2 = 56 + -56

Combine like terms: -6 + -56 = -62
-62 + -1x + x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-62 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + -1x + 62 + x2 = 0 + 62

Reorder the terms:
-62 + 62 + -1x + x2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + -1x + x2 = 0 + 62
-1x + x2 = 0 + 62

Combine like terms: 0 + 62 = 62
-1x + x2 = 62

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 62 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 62 + 0.25

Combine like terms: 62 + 0.25 = 62.25
0.25 + -1x + x2 = 62.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + -0.5) equal to 7.889866919 and -7.889866919.

Subproblem 1

x + -0.5 = 7.889866919 Simplifying x + -0.5 = 7.889866919 Reorder the terms: -0.5 + x = 7.889866919 Solving -0.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 7.889866919 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.889866919 + 0.5 x = 7.889866919 + 0.5 Combine like terms: 7.889866919 + 0.5 = 8.389866919 x = 8.389866919 Simplifying x = 8.389866919

Subproblem 2

x + -0.5 = -7.889866919 Simplifying x + -0.5 = -7.889866919 Reorder the terms: -0.5 + x = -7.889866919 Solving -0.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -7.889866919 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.889866919 + 0.5 x = -7.889866919 + 0.5 Combine like terms: -7.889866919 + 0.5 = -7.389866919 x = -7.389866919 Simplifying x = -7.389866919

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.389866919, -7.389866919}

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