2x+5=2x^2+8x+7

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Solution for 2x+5=2x^2+8x+7 equation:


Simplifying
2x + 5 = 2x2 + 8x + 7

Reorder the terms:
5 + 2x = 2x2 + 8x + 7

Reorder the terms:
5 + 2x = 7 + 8x + 2x2

Solving
5 + 2x = 7 + 8x + 2x2

Solving for variable 'x'.

Reorder the terms:
5 + -7 + 2x + -8x + -2x2 = 7 + 8x + 2x2 + -7 + -8x + -2x2

Combine like terms: 5 + -7 = -2
-2 + 2x + -8x + -2x2 = 7 + 8x + 2x2 + -7 + -8x + -2x2

Combine like terms: 2x + -8x = -6x
-2 + -6x + -2x2 = 7 + 8x + 2x2 + -7 + -8x + -2x2

Reorder the terms:
-2 + -6x + -2x2 = 7 + -7 + 8x + -8x + 2x2 + -2x2

Combine like terms: 7 + -7 = 0
-2 + -6x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
-2 + -6x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
-2 + -6x + -2x2 = 0 + 2x2 + -2x2
-2 + -6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-2 + -6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 3x + x2) = 0

Ignore the factor -2.

Subproblem 1

Set the factor '(1 + 3x + x2)' equal to zero and attempt to solve: Simplifying 1 + 3x + x2 = 0 Solving 1 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 3x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x + x2 = 0 + -1 3x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3x + x2 = -1 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -1 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -1 + 2.25 Combine like terms: -1 + 2.25 = 1.25 2.25 + 3x + x2 = 1.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + 1.5 = 1.118033989 Simplifying x + 1.5 = 1.118033989 Reorder the terms: 1.5 + x = 1.118033989 Solving 1.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.118033989 + -1.5 x = 1.118033989 + -1.5 Combine like terms: 1.118033989 + -1.5 = -0.381966011 x = -0.381966011 Simplifying x = -0.381966011

Subproblem 2

x + 1.5 = -1.118033989 Simplifying x + 1.5 = -1.118033989 Reorder the terms: 1.5 + x = -1.118033989 Solving 1.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.118033989 + -1.5 x = -1.118033989 + -1.5 Combine like terms: -1.118033989 + -1.5 = -2.618033989 x = -2.618033989 Simplifying x = -2.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.381966011, -2.618033989}

Solution

x = {-0.381966011, -2.618033989}

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