2x^2-3x-7=5x+1

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Solution for 2x^2-3x-7=5x+1 equation:


Simplifying
2x2 + -3x + -7 = 5x + 1

Reorder the terms:
-7 + -3x + 2x2 = 5x + 1

Reorder the terms:
-7 + -3x + 2x2 = 1 + 5x

Solving
-7 + -3x + 2x2 = 1 + 5x

Solving for variable 'x'.

Reorder the terms:
-7 + -1 + -3x + -5x + 2x2 = 1 + 5x + -1 + -5x

Combine like terms: -7 + -1 = -8
-8 + -3x + -5x + 2x2 = 1 + 5x + -1 + -5x

Combine like terms: -3x + -5x = -8x
-8 + -8x + 2x2 = 1 + 5x + -1 + -5x

Reorder the terms:
-8 + -8x + 2x2 = 1 + -1 + 5x + -5x

Combine like terms: 1 + -1 = 0
-8 + -8x + 2x2 = 0 + 5x + -5x
-8 + -8x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-8 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + -4x + x2)' equal to zero and attempt to solve: Simplifying -4 + -4x + x2 = 0 Solving -4 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -4x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -4x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4x + x2 = 0 + 4 -4x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4x + x2 = 4 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 = 4 + 4 Reorder the terms: 4 + -4x + x2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4x + x2 = 8 Factor a perfect square on the left side: (x + -2)(x + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -2) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + -2 = 2.828427125 Simplifying x + -2 = 2.828427125 Reorder the terms: -2 + x = 2.828427125 Solving -2 + x = 2.828427125 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 = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.828427125 + 2 x = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 x = 4.828427125 Simplifying x = 4.828427125

Subproblem 2

x + -2 = -2.828427125 Simplifying x + -2 = -2.828427125 Reorder the terms: -2 + x = -2.828427125 Solving -2 + x = -2.828427125 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 = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.828427125 + 2 x = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 x = -0.828427125 Simplifying x = -0.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.828427125, -0.828427125}

Solution

x = {4.828427125, -0.828427125}

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