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Simplifying 96x2 + -48x + -163 = 0 Reorder the terms: -163 + -48x + 96x2 = 0 Solving -163 + -48x + 96x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 96 the coefficient of the squared term: Divide each side by '96'. -1.697916667 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.697916667' to each side of the equation. -1.697916667 + -0.5x + 1.697916667 + x2 = 0 + 1.697916667 Reorder the terms: -1.697916667 + 1.697916667 + -0.5x + x2 = 0 + 1.697916667 Combine like terms: -1.697916667 + 1.697916667 = 0.000000000 0.000000000 + -0.5x + x2 = 0 + 1.697916667 -0.5x + x2 = 0 + 1.697916667 Combine like terms: 0 + 1.697916667 = 1.697916667 -0.5x + x2 = 1.697916667 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.697916667 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.697916667 + 0.0625 Combine like terms: 1.697916667 + 0.0625 = 1.760416667 0.0625 + -0.5x + x2 = 1.760416667 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.760416667 Calculate the square root of the right side: 1.326806944 Break this problem into two subproblems by setting (x + -0.25) equal to 1.326806944 and -1.326806944.Subproblem 1
x + -0.25 = 1.326806944 Simplifying x + -0.25 = 1.326806944 Reorder the terms: -0.25 + x = 1.326806944 Solving -0.25 + x = 1.326806944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.326806944 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.326806944 + 0.25 x = 1.326806944 + 0.25 Combine like terms: 1.326806944 + 0.25 = 1.576806944 x = 1.576806944 Simplifying x = 1.576806944Subproblem 2
x + -0.25 = -1.326806944 Simplifying x + -0.25 = -1.326806944 Reorder the terms: -0.25 + x = -1.326806944 Solving -0.25 + x = -1.326806944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.326806944 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.326806944 + 0.25 x = -1.326806944 + 0.25 Combine like terms: -1.326806944 + 0.25 = -1.076806944 x = -1.076806944 Simplifying x = -1.076806944Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.576806944, -1.076806944}
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