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Simplifying 2x2 + -2x = 1056 Reorder the terms: -2x + 2x2 = 1056 Solving -2x + 2x2 = 1056 Solving for variable 'x'. Reorder the terms: -1056 + -2x + 2x2 = 1056 + -1056 Combine like terms: 1056 + -1056 = 0 -1056 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-528 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-528 + -1x + x2)' equal to zero and attempt to solve: Simplifying -528 + -1x + x2 = 0 Solving -528 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '528' to each side of the equation. -528 + -1x + 528 + x2 = 0 + 528 Reorder the terms: -528 + 528 + -1x + x2 = 0 + 528 Combine like terms: -528 + 528 = 0 0 + -1x + x2 = 0 + 528 -1x + x2 = 0 + 528 Combine like terms: 0 + 528 = 528 -1x + x2 = 528 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 = 528 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 528 + 0.25 Combine like terms: 528 + 0.25 = 528.25 0.25 + -1x + x2 = 528.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 528.25 Calculate the square root of the right side: 22.983689869 Break this problem into two subproblems by setting (x + -0.5) equal to 22.983689869 and -22.983689869.Subproblem 1
x + -0.5 = 22.983689869 Simplifying x + -0.5 = 22.983689869 Reorder the terms: -0.5 + x = 22.983689869 Solving -0.5 + x = 22.983689869 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 = 22.983689869 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 22.983689869 + 0.5 x = 22.983689869 + 0.5 Combine like terms: 22.983689869 + 0.5 = 23.483689869 x = 23.483689869 Simplifying x = 23.483689869Subproblem 2
x + -0.5 = -22.983689869 Simplifying x + -0.5 = -22.983689869 Reorder the terms: -0.5 + x = -22.983689869 Solving -0.5 + x = -22.983689869 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 = -22.983689869 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -22.983689869 + 0.5 x = -22.983689869 + 0.5 Combine like terms: -22.983689869 + 0.5 = -22.483689869 x = -22.483689869 Simplifying x = -22.483689869Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.483689869, -22.483689869}Solution
x = {23.483689869, -22.483689869}
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