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Simplifying -0.008x2 + 0.939x + -0.975 = 0 Reorder the terms: -0.975 + 0.939x + -0.008x2 = 0 Solving -0.975 + 0.939x + -0.008x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.008 the coefficient of the squared term: Divide each side by '-0.008'. 121.875 + -117.375x + x2 = 0 Move the constant term to the right: Add '-121.875' to each side of the equation. 121.875 + -117.375x + -121.875 + x2 = 0 + -121.875 Reorder the terms: 121.875 + -121.875 + -117.375x + x2 = 0 + -121.875 Combine like terms: 121.875 + -121.875 = 0.000 0.000 + -117.375x + x2 = 0 + -121.875 -117.375x + x2 = 0 + -121.875 Combine like terms: 0 + -121.875 = -121.875 -117.375x + x2 = -121.875 The x term is -117.375x. Take half its coefficient (-58.6875). Square it (3444.222656) and add it to both sides. Add '3444.222656' to each side of the equation. -117.375x + 3444.222656 + x2 = -121.875 + 3444.222656 Reorder the terms: 3444.222656 + -117.375x + x2 = -121.875 + 3444.222656 Combine like terms: -121.875 + 3444.222656 = 3322.347656 3444.222656 + -117.375x + x2 = 3322.347656 Factor a perfect square on the left side: (x + -58.6875)(x + -58.6875) = 3322.347656 Calculate the square root of the right side: 57.639809646 Break this problem into two subproblems by setting (x + -58.6875) equal to 57.639809646 and -57.639809646.Subproblem 1
x + -58.6875 = 57.639809646 Simplifying x + -58.6875 = 57.639809646 Reorder the terms: -58.6875 + x = 57.639809646 Solving -58.6875 + x = 57.639809646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.6875' to each side of the equation. -58.6875 + 58.6875 + x = 57.639809646 + 58.6875 Combine like terms: -58.6875 + 58.6875 = 0.0000 0.0000 + x = 57.639809646 + 58.6875 x = 57.639809646 + 58.6875 Combine like terms: 57.639809646 + 58.6875 = 116.327309646 x = 116.327309646 Simplifying x = 116.327309646Subproblem 2
x + -58.6875 = -57.639809646 Simplifying x + -58.6875 = -57.639809646 Reorder the terms: -58.6875 + x = -57.639809646 Solving -58.6875 + x = -57.639809646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.6875' to each side of the equation. -58.6875 + 58.6875 + x = -57.639809646 + 58.6875 Combine like terms: -58.6875 + 58.6875 = 0.0000 0.0000 + x = -57.639809646 + 58.6875 x = -57.639809646 + 58.6875 Combine like terms: -57.639809646 + 58.6875 = 1.047690354 x = 1.047690354 Simplifying x = 1.047690354Solution
The solution to the problem is based on the solutions from the subproblems. x = {116.327309646, 1.047690354}
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