x^2+2x+12(x^2+2x)=7

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Solution for x^2+2x+12(x^2+2x)=7 equation:


Simplifying
x2 + 2x + 12(x2 + 2x) = 7

Reorder the terms:
x2 + 2x + 12(2x + x2) = 7
x2 + 2x + (2x * 12 + x2 * 12) = 7
x2 + 2x + (24x + 12x2) = 7

Reorder the terms:
2x + 24x + x2 + 12x2 = 7

Combine like terms: 2x + 24x = 26x
26x + x2 + 12x2 = 7

Combine like terms: x2 + 12x2 = 13x2
26x + 13x2 = 7

Solving
26x + 13x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 26x + 13x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 26x + 13x2 = 0

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

Divide each side by '13'.
-0.5384615385 + 2x + x2 = 0

Move the constant term to the right:

Add '0.5384615385' to each side of the equation.
-0.5384615385 + 2x + 0.5384615385 + x2 = 0 + 0.5384615385

Reorder the terms:
-0.5384615385 + 0.5384615385 + 2x + x2 = 0 + 0.5384615385

Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + 0.5384615385
2x + x2 = 0 + 0.5384615385

Combine like terms: 0 + 0.5384615385 = 0.5384615385
2x + x2 = 0.5384615385

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 0.5384615385 + 1

Reorder the terms:
1 + 2x + x2 = 0.5384615385 + 1

Combine like terms: 0.5384615385 + 1 = 1.5384615385
1 + 2x + x2 = 1.5384615385

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.5384615385

Calculate the square root of the right side: 1.240347346

Break this problem into two subproblems by setting 
(x + 1) equal to 1.240347346 and -1.240347346.

Subproblem 1

x + 1 = 1.240347346 Simplifying x + 1 = 1.240347346 Reorder the terms: 1 + x = 1.240347346 Solving 1 + x = 1.240347346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.240347346 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.240347346 + -1 x = 1.240347346 + -1 Combine like terms: 1.240347346 + -1 = 0.240347346 x = 0.240347346 Simplifying x = 0.240347346

Subproblem 2

x + 1 = -1.240347346 Simplifying x + 1 = -1.240347346 Reorder the terms: 1 + x = -1.240347346 Solving 1 + x = -1.240347346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.240347346 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.240347346 + -1 x = -1.240347346 + -1 Combine like terms: -1.240347346 + -1 = -2.240347346 x = -2.240347346 Simplifying x = -2.240347346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.240347346, -2.240347346}

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