2x^2=2x+6

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Solution for 2x^2=2x+6 equation:


Simplifying
2x2 = 2x + 6

Reorder the terms:
2x2 = 6 + 2x

Solving
2x2 = 6 + 2x

Solving for variable 'x'.

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

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

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

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

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -1x + x2)' equal to zero and attempt to solve: Simplifying -3 + -1x + x2 = 0 Solving -3 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -1x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -1x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x + x2 = 0 + 3 -1x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1x + x2 = 3 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 3 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + -1x + x2 = 3.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + -0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

x + -0.5 = 1.802775638 Simplifying x + -0.5 = 1.802775638 Reorder the terms: -0.5 + x = 1.802775638 Solving -0.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.802775638 + 0.5 x = 1.802775638 + 0.5 Combine like terms: 1.802775638 + 0.5 = 2.302775638 x = 2.302775638 Simplifying x = 2.302775638

Subproblem 2

x + -0.5 = -1.802775638 Simplifying x + -0.5 = -1.802775638 Reorder the terms: -0.5 + x = -1.802775638 Solving -0.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.802775638 + 0.5 x = -1.802775638 + 0.5 Combine like terms: -1.802775638 + 0.5 = -1.302775638 x = -1.302775638 Simplifying x = -1.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.302775638, -1.302775638}

Solution

x = {2.302775638, -1.302775638}

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