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Simplifying 8x(x + -100) = 112 Reorder the terms: 8x(-100 + x) = 112 (-100 * 8x + x * 8x) = 112 (-800x + 8x2) = 112 Solving -800x + 8x2 = 112 Solving for variable 'x'. Reorder the terms: -112 + -800x + 8x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + -800x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-14 + -100x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-14 + -100x + x2)' equal to zero and attempt to solve: Simplifying -14 + -100x + x2 = 0 Solving -14 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -100x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -100x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -100x + x2 = 0 + 14 -100x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -100x + x2 = 14 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = 14 + 2500 Reorder the terms: 2500 + -100x + x2 = 14 + 2500 Combine like terms: 14 + 2500 = 2514 2500 + -100x + x2 = 2514 Factor a perfect square on the left side: (x + -50)(x + -50) = 2514 Calculate the square root of the right side: 50.139804547 Break this problem into two subproblems by setting (x + -50) equal to 50.139804547 and -50.139804547.Subproblem 1
x + -50 = 50.139804547 Simplifying x + -50 = 50.139804547 Reorder the terms: -50 + x = 50.139804547 Solving -50 + x = 50.139804547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 50.139804547 + 50 Combine like terms: -50 + 50 = 0 0 + x = 50.139804547 + 50 x = 50.139804547 + 50 Combine like terms: 50.139804547 + 50 = 100.139804547 x = 100.139804547 Simplifying x = 100.139804547Subproblem 2
x + -50 = -50.139804547 Simplifying x + -50 = -50.139804547 Reorder the terms: -50 + x = -50.139804547 Solving -50 + x = -50.139804547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -50.139804547 + 50 Combine like terms: -50 + 50 = 0 0 + x = -50.139804547 + 50 x = -50.139804547 + 50 Combine like terms: -50.139804547 + 50 = -0.139804547 x = -0.139804547 Simplifying x = -0.139804547Solution
The solution to the problem is based on the solutions from the subproblems. x = {100.139804547, -0.139804547}Solution
x = {100.139804547, -0.139804547}
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