(5+x)(x-2)=40

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Solution for (5+x)(x-2)=40 equation:


Simplifying
(5 + x)(x + -2) = 40

Reorder the terms:
(5 + x)(-2 + x) = 40

Multiply (5 + x) * (-2 + x)
(5(-2 + x) + x(-2 + x)) = 40
((-2 * 5 + x * 5) + x(-2 + x)) = 40
((-10 + 5x) + x(-2 + x)) = 40
(-10 + 5x + (-2 * x + x * x)) = 40
(-10 + 5x + (-2x + x2)) = 40

Combine like terms: 5x + -2x = 3x
(-10 + 3x + x2) = 40

Solving
-10 + 3x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
-10 + -40 + 3x + x2 = 40 + -40

Combine like terms: -10 + -40 = -50
-50 + 3x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-50 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 3x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 3x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 3x + x2 = 0 + 50
3x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
3x + x2 = 50

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 50 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 50 + 2.25

Combine like terms: 50 + 2.25 = 52.25
2.25 + 3x + x2 = 52.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(x + 1.5) equal to 7.228416147 and -7.228416147.

Subproblem 1

x + 1.5 = 7.228416147 Simplifying x + 1.5 = 7.228416147 Reorder the terms: 1.5 + x = 7.228416147 Solving 1.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.228416147 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.228416147 + -1.5 x = 7.228416147 + -1.5 Combine like terms: 7.228416147 + -1.5 = 5.728416147 x = 5.728416147 Simplifying x = 5.728416147

Subproblem 2

x + 1.5 = -7.228416147 Simplifying x + 1.5 = -7.228416147 Reorder the terms: 1.5 + x = -7.228416147 Solving 1.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.228416147 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.228416147 + -1.5 x = -7.228416147 + -1.5 Combine like terms: -7.228416147 + -1.5 = -8.728416147 x = -8.728416147 Simplifying x = -8.728416147

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.728416147, -8.728416147}

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