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Simplifying -16x2 + 880x + 70.7 = 0 Reorder the terms: 70.7 + 880x + -16x2 = 0 Solving 70.7 + 880x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -4.41875 + -55x + x2 = 0 Move the constant term to the right: Add '4.41875' to each side of the equation. -4.41875 + -55x + 4.41875 + x2 = 0 + 4.41875 Reorder the terms: -4.41875 + 4.41875 + -55x + x2 = 0 + 4.41875 Combine like terms: -4.41875 + 4.41875 = 0.00000 0.00000 + -55x + x2 = 0 + 4.41875 -55x + x2 = 0 + 4.41875 Combine like terms: 0 + 4.41875 = 4.41875 -55x + x2 = 4.41875 The x term is -55x. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55x + 756.25 + x2 = 4.41875 + 756.25 Reorder the terms: 756.25 + -55x + x2 = 4.41875 + 756.25 Combine like terms: 4.41875 + 756.25 = 760.66875 756.25 + -55x + x2 = 760.66875 Factor a perfect square on the left side: (x + -27.5)(x + -27.5) = 760.66875 Calculate the square root of the right side: 27.580223893 Break this problem into two subproblems by setting (x + -27.5) equal to 27.580223893 and -27.580223893.Subproblem 1
x + -27.5 = 27.580223893 Simplifying x + -27.5 = 27.580223893 Reorder the terms: -27.5 + x = 27.580223893 Solving -27.5 + x = 27.580223893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = 27.580223893 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = 27.580223893 + 27.5 x = 27.580223893 + 27.5 Combine like terms: 27.580223893 + 27.5 = 55.080223893 x = 55.080223893 Simplifying x = 55.080223893Subproblem 2
x + -27.5 = -27.580223893 Simplifying x + -27.5 = -27.580223893 Reorder the terms: -27.5 + x = -27.580223893 Solving -27.5 + x = -27.580223893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = -27.580223893 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = -27.580223893 + 27.5 x = -27.580223893 + 27.5 Combine like terms: -27.580223893 + 27.5 = -0.080223893 x = -0.080223893 Simplifying x = -0.080223893Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.080223893, -0.080223893}
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