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Simplifying 2x2 + 10x = 768 Reorder the terms: 10x + 2x2 = 768 Solving 10x + 2x2 = 768 Solving for variable 'x'. Reorder the terms: -768 + 10x + 2x2 = 768 + -768 Combine like terms: 768 + -768 = 0 -768 + 10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-384 + 5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-384 + 5x + x2)' equal to zero and attempt to solve: Simplifying -384 + 5x + x2 = 0 Solving -384 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '384' to each side of the equation. -384 + 5x + 384 + x2 = 0 + 384 Reorder the terms: -384 + 384 + 5x + x2 = 0 + 384 Combine like terms: -384 + 384 = 0 0 + 5x + x2 = 0 + 384 5x + x2 = 0 + 384 Combine like terms: 0 + 384 = 384 5x + x2 = 384 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 384 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 384 + 6.25 Combine like terms: 384 + 6.25 = 390.25 6.25 + 5x + x2 = 390.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 390.25 Calculate the square root of the right side: 19.754746265 Break this problem into two subproblems by setting (x + 2.5) equal to 19.754746265 and -19.754746265.Subproblem 1
x + 2.5 = 19.754746265 Simplifying x + 2.5 = 19.754746265 Reorder the terms: 2.5 + x = 19.754746265 Solving 2.5 + x = 19.754746265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 19.754746265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 19.754746265 + -2.5 x = 19.754746265 + -2.5 Combine like terms: 19.754746265 + -2.5 = 17.254746265 x = 17.254746265 Simplifying x = 17.254746265Subproblem 2
x + 2.5 = -19.754746265 Simplifying x + 2.5 = -19.754746265 Reorder the terms: 2.5 + x = -19.754746265 Solving 2.5 + x = -19.754746265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -19.754746265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -19.754746265 + -2.5 x = -19.754746265 + -2.5 Combine like terms: -19.754746265 + -2.5 = -22.254746265 x = -22.254746265 Simplifying x = -22.254746265Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.254746265, -22.254746265}Solution
x = {17.254746265, -22.254746265}
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