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

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


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -3 + -7 = -10
-10 + -7x + x + 2x2 = 7 + -1x + -7 + x

Combine like terms: -7x + x = -6x
-10 + -6x + 2x2 = 7 + -1x + -7 + x

Reorder the terms:
-10 + -6x + 2x2 = 7 + -7 + -1x + x

Combine like terms: 7 + -7 = 0
-10 + -6x + 2x2 = 0 + -1x + x
-10 + -6x + 2x2 = -1x + x

Combine like terms: -1x + x = 0
-10 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -3x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -3x + x2)' equal to zero and attempt to solve: Simplifying -5 + -3x + x2 = 0 Solving -5 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -3x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -3x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3x + x2 = 0 + 5 -3x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3x + x2 = 5 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 = 5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 5 + 2.25 Combine like terms: 5 + 2.25 = 7.25 2.25 + -3x + x2 = 7.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1

x + -1.5 = 2.692582404 Simplifying x + -1.5 = 2.692582404 Reorder the terms: -1.5 + x = 2.692582404 Solving -1.5 + x = 2.692582404 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 = 2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.692582404 + 1.5 x = 2.692582404 + 1.5 Combine like terms: 2.692582404 + 1.5 = 4.192582404 x = 4.192582404 Simplifying x = 4.192582404

Subproblem 2

x + -1.5 = -2.692582404 Simplifying x + -1.5 = -2.692582404 Reorder the terms: -1.5 + x = -2.692582404 Solving -1.5 + x = -2.692582404 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 = -2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.692582404 + 1.5 x = -2.692582404 + 1.5 Combine like terms: -2.692582404 + 1.5 = -1.192582404 x = -1.192582404 Simplifying x = -1.192582404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.192582404, -1.192582404}

Solution

x = {4.192582404, -1.192582404}

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