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Simplifying -16x2 + 116x + 84 = 125 Reorder the terms: 84 + 116x + -16x2 = 125 Solving 84 + 116x + -16x2 = 125 Solving for variable 'x'. Reorder the terms: 84 + -125 + 116x + -16x2 = 125 + -125 Combine like terms: 84 + -125 = -41 -41 + 116x + -16x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -41 + 116x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 2.5625 + -7.25x + x2 = 0 Move the constant term to the right: Add '-2.5625' to each side of the equation. 2.5625 + -7.25x + -2.5625 + x2 = 0 + -2.5625 Reorder the terms: 2.5625 + -2.5625 + -7.25x + x2 = 0 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + -7.25x + x2 = 0 + -2.5625 -7.25x + x2 = 0 + -2.5625 Combine like terms: 0 + -2.5625 = -2.5625 -7.25x + x2 = -2.5625 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = -2.5625 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = -2.5625 + 13.140625 Combine like terms: -2.5625 + 13.140625 = 10.578125 13.140625 + -7.25x + x2 = 10.578125 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 10.578125 Calculate the square root of the right side: 3.252402958 Break this problem into two subproblems by setting (x + -3.625) equal to 3.252402958 and -3.252402958.Subproblem 1
x + -3.625 = 3.252402958 Simplifying x + -3.625 = 3.252402958 Reorder the terms: -3.625 + x = 3.252402958 Solving -3.625 + x = 3.252402958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 3.252402958 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 3.252402958 + 3.625 x = 3.252402958 + 3.625 Combine like terms: 3.252402958 + 3.625 = 6.877402958 x = 6.877402958 Simplifying x = 6.877402958Subproblem 2
x + -3.625 = -3.252402958 Simplifying x + -3.625 = -3.252402958 Reorder the terms: -3.625 + x = -3.252402958 Solving -3.625 + x = -3.252402958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -3.252402958 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -3.252402958 + 3.625 x = -3.252402958 + 3.625 Combine like terms: -3.252402958 + 3.625 = 0.372597042 x = 0.372597042 Simplifying x = 0.372597042Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.877402958, 0.372597042}
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