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Simplifying 0 = -16x2 + 215x + -95 Reorder the terms: 0 = -95 + 215x + -16x2 Solving 0 = -95 + 215x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 95 = 95 95 + -215x + 16x2 = -95 + 215x + -16x2 + 95 + -215x + 16x2 Reorder the terms: 95 + -215x + 16x2 = -95 + 95 + 215x + -215x + -16x2 + 16x2 Combine like terms: -95 + 95 = 0 95 + -215x + 16x2 = 0 + 215x + -215x + -16x2 + 16x2 95 + -215x + 16x2 = 215x + -215x + -16x2 + 16x2 Combine like terms: 215x + -215x = 0 95 + -215x + 16x2 = 0 + -16x2 + 16x2 95 + -215x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 95 + -215x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.9375 + -13.4375x + x2 = 0 Move the constant term to the right: Add '-5.9375' to each side of the equation. 5.9375 + -13.4375x + -5.9375 + x2 = 0 + -5.9375 Reorder the terms: 5.9375 + -5.9375 + -13.4375x + x2 = 0 + -5.9375 Combine like terms: 5.9375 + -5.9375 = 0.0000 0.0000 + -13.4375x + x2 = 0 + -5.9375 -13.4375x + x2 = 0 + -5.9375 Combine like terms: 0 + -5.9375 = -5.9375 -13.4375x + x2 = -5.9375 The x term is -13.4375x. Take half its coefficient (-6.71875). Square it (45.14160156) and add it to both sides. Add '45.14160156' to each side of the equation. -13.4375x + 45.14160156 + x2 = -5.9375 + 45.14160156 Reorder the terms: 45.14160156 + -13.4375x + x2 = -5.9375 + 45.14160156 Combine like terms: -5.9375 + 45.14160156 = 39.20410156 45.14160156 + -13.4375x + x2 = 39.20410156 Factor a perfect square on the left side: (x + -6.71875)(x + -6.71875) = 39.20410156 Calculate the square root of the right side: 6.261317877 Break this problem into two subproblems by setting (x + -6.71875) equal to 6.261317877 and -6.261317877.Subproblem 1
x + -6.71875 = 6.261317877 Simplifying x + -6.71875 = 6.261317877 Reorder the terms: -6.71875 + x = 6.261317877 Solving -6.71875 + x = 6.261317877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.71875' to each side of the equation. -6.71875 + 6.71875 + x = 6.261317877 + 6.71875 Combine like terms: -6.71875 + 6.71875 = 0.00000 0.00000 + x = 6.261317877 + 6.71875 x = 6.261317877 + 6.71875 Combine like terms: 6.261317877 + 6.71875 = 12.980067877 x = 12.980067877 Simplifying x = 12.980067877Subproblem 2
x + -6.71875 = -6.261317877 Simplifying x + -6.71875 = -6.261317877 Reorder the terms: -6.71875 + x = -6.261317877 Solving -6.71875 + x = -6.261317877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.71875' to each side of the equation. -6.71875 + 6.71875 + x = -6.261317877 + 6.71875 Combine like terms: -6.71875 + 6.71875 = 0.00000 0.00000 + x = -6.261317877 + 6.71875 x = -6.261317877 + 6.71875 Combine like terms: -6.261317877 + 6.71875 = 0.457432123 x = 0.457432123 Simplifying x = 0.457432123Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.980067877, 0.457432123}
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