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Simplifying 4x2 + -58x + 135 = 0 Reorder the terms: 135 + -58x + 4x2 = 0 Solving 135 + -58x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 33.75 + -14.5x + x2 = 0 Move the constant term to the right: Add '-33.75' to each side of the equation. 33.75 + -14.5x + -33.75 + x2 = 0 + -33.75 Reorder the terms: 33.75 + -33.75 + -14.5x + x2 = 0 + -33.75 Combine like terms: 33.75 + -33.75 = 0.00 0.00 + -14.5x + x2 = 0 + -33.75 -14.5x + x2 = 0 + -33.75 Combine like terms: 0 + -33.75 = -33.75 -14.5x + x2 = -33.75 The x term is -14.5x. Take half its coefficient (-7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. -14.5x + 52.5625 + x2 = -33.75 + 52.5625 Reorder the terms: 52.5625 + -14.5x + x2 = -33.75 + 52.5625 Combine like terms: -33.75 + 52.5625 = 18.8125 52.5625 + -14.5x + x2 = 18.8125 Factor a perfect square on the left side: (x + -7.25)(x + -7.25) = 18.8125 Calculate the square root of the right side: 4.337337893 Break this problem into two subproblems by setting (x + -7.25) equal to 4.337337893 and -4.337337893.Subproblem 1
x + -7.25 = 4.337337893 Simplifying x + -7.25 = 4.337337893 Reorder the terms: -7.25 + x = 4.337337893 Solving -7.25 + x = 4.337337893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = 4.337337893 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 4.337337893 + 7.25 x = 4.337337893 + 7.25 Combine like terms: 4.337337893 + 7.25 = 11.587337893 x = 11.587337893 Simplifying x = 11.587337893Subproblem 2
x + -7.25 = -4.337337893 Simplifying x + -7.25 = -4.337337893 Reorder the terms: -7.25 + x = -4.337337893 Solving -7.25 + x = -4.337337893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = -4.337337893 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -4.337337893 + 7.25 x = -4.337337893 + 7.25 Combine like terms: -4.337337893 + 7.25 = 2.912662107 x = 2.912662107 Simplifying x = 2.912662107Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.587337893, 2.912662107}
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