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Simplifying 0 = x2 + 95x + -40 Reorder the terms: 0 = -40 + 95x + x2 Solving 0 = -40 + 95x + x2 Solving for variable 'x'. Combine like terms: 0 + 40 = 40 40 + -95x + -1x2 = -40 + 95x + x2 + 40 + -95x + -1x2 Reorder the terms: 40 + -95x + -1x2 = -40 + 40 + 95x + -95x + x2 + -1x2 Combine like terms: -40 + 40 = 0 40 + -95x + -1x2 = 0 + 95x + -95x + x2 + -1x2 40 + -95x + -1x2 = 95x + -95x + x2 + -1x2 Combine like terms: 95x + -95x = 0 40 + -95x + -1x2 = 0 + x2 + -1x2 40 + -95x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40 + -95x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 95x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 95x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 95x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 95x + x2 = 0 + 40 95x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 95x + x2 = 40 The x term is 95x. Take half its coefficient (47.5). Square it (2256.25) and add it to both sides. Add '2256.25' to each side of the equation. 95x + 2256.25 + x2 = 40 + 2256.25 Reorder the terms: 2256.25 + 95x + x2 = 40 + 2256.25 Combine like terms: 40 + 2256.25 = 2296.25 2256.25 + 95x + x2 = 2296.25 Factor a perfect square on the left side: (x + 47.5)(x + 47.5) = 2296.25 Calculate the square root of the right side: 47.919202831 Break this problem into two subproblems by setting (x + 47.5) equal to 47.919202831 and -47.919202831.Subproblem 1
x + 47.5 = 47.919202831 Simplifying x + 47.5 = 47.919202831 Reorder the terms: 47.5 + x = 47.919202831 Solving 47.5 + x = 47.919202831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + x = 47.919202831 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + x = 47.919202831 + -47.5 x = 47.919202831 + -47.5 Combine like terms: 47.919202831 + -47.5 = 0.419202831 x = 0.419202831 Simplifying x = 0.419202831Subproblem 2
x + 47.5 = -47.919202831 Simplifying x + 47.5 = -47.919202831 Reorder the terms: 47.5 + x = -47.919202831 Solving 47.5 + x = -47.919202831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + x = -47.919202831 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + x = -47.919202831 + -47.5 x = -47.919202831 + -47.5 Combine like terms: -47.919202831 + -47.5 = -95.419202831 x = -95.419202831 Simplifying x = -95.419202831Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.419202831, -95.419202831}
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