7x+100=x^2-90

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Solution for 7x+100=x^2-90 equation:


Simplifying
7x + 100 = x2 + -90

Reorder the terms:
100 + 7x = x2 + -90

Reorder the terms:
100 + 7x = -90 + x2

Solving
100 + 7x = -90 + x2

Solving for variable 'x'.

Reorder the terms:
100 + 90 + 7x + -1x2 = -90 + x2 + 90 + -1x2

Combine like terms: 100 + 90 = 190
190 + 7x + -1x2 = -90 + x2 + 90 + -1x2

Reorder the terms:
190 + 7x + -1x2 = -90 + 90 + x2 + -1x2

Combine like terms: -90 + 90 = 0
190 + 7x + -1x2 = 0 + x2 + -1x2
190 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
190 + 7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-190 + -7x + x2 = 0

Move the constant term to the right:

Add '190' to each side of the equation.
-190 + -7x + 190 + x2 = 0 + 190

Reorder the terms:
-190 + 190 + -7x + x2 = 0 + 190

Combine like terms: -190 + 190 = 0
0 + -7x + x2 = 0 + 190
-7x + x2 = 0 + 190

Combine like terms: 0 + 190 = 190
-7x + x2 = 190

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 190 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 190 + 12.25

Combine like terms: 190 + 12.25 = 202.25
12.25 + -7x + x2 = 202.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 202.25

Calculate the square root of the right side: 14.221462653

Break this problem into two subproblems by setting 
(x + -3.5) equal to 14.221462653 and -14.221462653.

Subproblem 1

x + -3.5 = 14.221462653 Simplifying x + -3.5 = 14.221462653 Reorder the terms: -3.5 + x = 14.221462653 Solving -3.5 + x = 14.221462653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 14.221462653 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 14.221462653 + 3.5 x = 14.221462653 + 3.5 Combine like terms: 14.221462653 + 3.5 = 17.721462653 x = 17.721462653 Simplifying x = 17.721462653

Subproblem 2

x + -3.5 = -14.221462653 Simplifying x + -3.5 = -14.221462653 Reorder the terms: -3.5 + x = -14.221462653 Solving -3.5 + x = -14.221462653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -14.221462653 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -14.221462653 + 3.5 x = -14.221462653 + 3.5 Combine like terms: -14.221462653 + 3.5 = -10.721462653 x = -10.721462653 Simplifying x = -10.721462653

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.721462653, -10.721462653}

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