8x=x^2+4x-3

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Solution for 8x=x^2+4x-3 equation:


Simplifying
8x = x2 + 4x + -3

Reorder the terms:
8x = -3 + 4x + x2

Solving
8x = -3 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
3 + 8x + -4x + -1x2 = -3 + 4x + x2 + 3 + -4x + -1x2

Combine like terms: 8x + -4x = 4x
3 + 4x + -1x2 = -3 + 4x + x2 + 3 + -4x + -1x2

Reorder the terms:
3 + 4x + -1x2 = -3 + 3 + 4x + -4x + x2 + -1x2

Combine like terms: -3 + 3 = 0
3 + 4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
3 + 4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
3 + 4x + -1x2 = 0 + x2 + -1x2
3 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + 4x + -1x2 = 0

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

Divide each side by '-1'.
-3 + -4x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -4x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x + x2 = 0 + 3
-4x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4x + x2 = 3

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 3 + 4

Reorder the terms:
4 + -4x + x2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + -4x + x2 = 7

Factor a perfect square on the left side:
(x + -2)(x + -2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -2) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + -2 = 2.645751311 Simplifying x + -2 = 2.645751311 Reorder the terms: -2 + x = 2.645751311 Solving -2 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.645751311 + 2 x = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 x = 4.645751311 Simplifying x = 4.645751311

Subproblem 2

x + -2 = -2.645751311 Simplifying x + -2 = -2.645751311 Reorder the terms: -2 + x = -2.645751311 Solving -2 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.645751311 + 2 x = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 x = -0.645751311 Simplifying x = -0.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.645751311, -0.645751311}

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