(x+5)(x-10)=35

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Solution for (x+5)(x-10)=35 equation:


Simplifying
(x + 5)(x + -10) = 35

Reorder the terms:
(5 + x)(x + -10) = 35

Reorder the terms:
(5 + x)(-10 + x) = 35

Multiply (5 + x) * (-10 + x)
(5(-10 + x) + x(-10 + x)) = 35
((-10 * 5 + x * 5) + x(-10 + x)) = 35
((-50 + 5x) + x(-10 + x)) = 35
(-50 + 5x + (-10 * x + x * x)) = 35
(-50 + 5x + (-10x + x2)) = 35

Combine like terms: 5x + -10x = -5x
(-50 + -5x + x2) = 35

Solving
-50 + -5x + x2 = 35

Solving for variable 'x'.

Reorder the terms:
-50 + -35 + -5x + x2 = 35 + -35

Combine like terms: -50 + -35 = -85
-85 + -5x + x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-85 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + -5x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + -5x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + -5x + x2 = 0 + 85
-5x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
-5x + x2 = 85

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 85 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 85 + 6.25

Combine like terms: 85 + 6.25 = 91.25
6.25 + -5x + x2 = 91.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 91.25

Calculate the square root of the right side: 9.552486587

Break this problem into two subproblems by setting 
(x + -2.5) equal to 9.552486587 and -9.552486587.

Subproblem 1

x + -2.5 = 9.552486587 Simplifying x + -2.5 = 9.552486587 Reorder the terms: -2.5 + x = 9.552486587 Solving -2.5 + x = 9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 9.552486587 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 9.552486587 + 2.5 x = 9.552486587 + 2.5 Combine like terms: 9.552486587 + 2.5 = 12.052486587 x = 12.052486587 Simplifying x = 12.052486587

Subproblem 2

x + -2.5 = -9.552486587 Simplifying x + -2.5 = -9.552486587 Reorder the terms: -2.5 + x = -9.552486587 Solving -2.5 + x = -9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -9.552486587 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -9.552486587 + 2.5 x = -9.552486587 + 2.5 Combine like terms: -9.552486587 + 2.5 = -7.052486587 x = -7.052486587 Simplifying x = -7.052486587

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.052486587, -7.052486587}

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