x^2+10x+7=2x-4

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Solution for x^2+10x+7=2x-4 equation:


Simplifying
x2 + 10x + 7 = 2x + -4

Reorder the terms:
7 + 10x + x2 = 2x + -4

Reorder the terms:
7 + 10x + x2 = -4 + 2x

Solving
7 + 10x + x2 = -4 + 2x

Solving for variable 'x'.

Reorder the terms:
7 + 4 + 10x + -2x + x2 = -4 + 2x + 4 + -2x

Combine like terms: 7 + 4 = 11
11 + 10x + -2x + x2 = -4 + 2x + 4 + -2x

Combine like terms: 10x + -2x = 8x
11 + 8x + x2 = -4 + 2x + 4 + -2x

Reorder the terms:
11 + 8x + x2 = -4 + 4 + 2x + -2x

Combine like terms: -4 + 4 = 0
11 + 8x + x2 = 0 + 2x + -2x
11 + 8x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
11 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 8x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 8x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 8x + x2 = 0 + -11
8x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
8x + x2 = -11

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -11 + 16

Reorder the terms:
16 + 8x + x2 = -11 + 16

Combine like terms: -11 + 16 = 5
16 + 8x + x2 = 5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 4) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + 4 = 2.236067978 Simplifying x + 4 = 2.236067978 Reorder the terms: 4 + x = 2.236067978 Solving 4 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 2.236067978 + -4 Combine like terms: 4 + -4 = 0 0 + x = 2.236067978 + -4 x = 2.236067978 + -4 Combine like terms: 2.236067978 + -4 = -1.763932022 x = -1.763932022 Simplifying x = -1.763932022

Subproblem 2

x + 4 = -2.236067978 Simplifying x + 4 = -2.236067978 Reorder the terms: 4 + x = -2.236067978 Solving 4 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -2.236067978 + -4 Combine like terms: 4 + -4 = 0 0 + x = -2.236067978 + -4 x = -2.236067978 + -4 Combine like terms: -2.236067978 + -4 = -6.236067978 x = -6.236067978 Simplifying x = -6.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.763932022, -6.236067978}

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