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Simplifying 57.6x2 + 8x + -90 = 0 Reorder the terms: -90 + 8x + 57.6x2 = 0 Solving -90 + 8x + 57.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 57.6 the coefficient of the squared term: Divide each side by '57.6'. -1.5625 + 0.1388888889x + x2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 0.1388888889x + 1.5625 + x2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 0.1388888889x + x2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 0.1388888889x + x2 = 0 + 1.5625 0.1388888889x + x2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 0.1388888889x + x2 = 1.5625 The x term is 0.1388888889x. Take half its coefficient (0.06944444445). Square it (0.004822530865) and add it to both sides. Add '0.004822530865' to each side of the equation. 0.1388888889x + 0.004822530865 + x2 = 1.5625 + 0.004822530865 Reorder the terms: 0.004822530865 + 0.1388888889x + x2 = 1.5625 + 0.004822530865 Combine like terms: 1.5625 + 0.004822530865 = 1.567322530865 0.004822530865 + 0.1388888889x + x2 = 1.567322530865 Factor a perfect square on the left side: (x + 0.06944444445)(x + 0.06944444445) = 1.567322530865 Calculate the square root of the right side: 1.251927526 Break this problem into two subproblems by setting (x + 0.06944444445) equal to 1.251927526 and -1.251927526.Subproblem 1
x + 0.06944444445 = 1.251927526 Simplifying x + 0.06944444445 = 1.251927526 Reorder the terms: 0.06944444445 + x = 1.251927526 Solving 0.06944444445 + x = 1.251927526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06944444445' to each side of the equation. 0.06944444445 + -0.06944444445 + x = 1.251927526 + -0.06944444445 Combine like terms: 0.06944444445 + -0.06944444445 = 0.00000000000 0.00000000000 + x = 1.251927526 + -0.06944444445 x = 1.251927526 + -0.06944444445 Combine like terms: 1.251927526 + -0.06944444445 = 1.18248308155 x = 1.18248308155 Simplifying x = 1.18248308155Subproblem 2
x + 0.06944444445 = -1.251927526 Simplifying x + 0.06944444445 = -1.251927526 Reorder the terms: 0.06944444445 + x = -1.251927526 Solving 0.06944444445 + x = -1.251927526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06944444445' to each side of the equation. 0.06944444445 + -0.06944444445 + x = -1.251927526 + -0.06944444445 Combine like terms: 0.06944444445 + -0.06944444445 = 0.00000000000 0.00000000000 + x = -1.251927526 + -0.06944444445 x = -1.251927526 + -0.06944444445 Combine like terms: -1.251927526 + -0.06944444445 = -1.32137197045 x = -1.32137197045 Simplifying x = -1.32137197045Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.18248308155, -1.32137197045}
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