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Simplifying x = 112 + 96x + -16x2 Solving x = 112 + 96x + -16x2 Solving for variable 'x'. Reorder the terms: -112 + x + -96x + 16x2 = 112 + 96x + -16x2 + -112 + -96x + 16x2 Combine like terms: x + -96x = -95x -112 + -95x + 16x2 = 112 + 96x + -16x2 + -112 + -96x + 16x2 Reorder the terms: -112 + -95x + 16x2 = 112 + -112 + 96x + -96x + -16x2 + 16x2 Combine like terms: 112 + -112 = 0 -112 + -95x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2 -112 + -95x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 -112 + -95x + 16x2 = 0 + -16x2 + 16x2 -112 + -95x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -112 + -95x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -7 + -5.9375x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -5.9375x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -5.9375x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5.9375x + x2 = 0 + 7 -5.9375x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5.9375x + x2 = 7 The x term is -5.9375x. Take half its coefficient (-2.96875). Square it (8.813476563) and add it to both sides. Add '8.813476563' to each side of the equation. -5.9375x + 8.813476563 + x2 = 7 + 8.813476563 Reorder the terms: 8.813476563 + -5.9375x + x2 = 7 + 8.813476563 Combine like terms: 7 + 8.813476563 = 15.813476563 8.813476563 + -5.9375x + x2 = 15.813476563 Factor a perfect square on the left side: (x + -2.96875)(x + -2.96875) = 15.813476563 Calculate the square root of the right side: 3.97661622 Break this problem into two subproblems by setting (x + -2.96875) equal to 3.97661622 and -3.97661622.Subproblem 1
x + -2.96875 = 3.97661622 Simplifying x + -2.96875 = 3.97661622 Reorder the terms: -2.96875 + x = 3.97661622 Solving -2.96875 + x = 3.97661622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = 3.97661622 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = 3.97661622 + 2.96875 x = 3.97661622 + 2.96875 Combine like terms: 3.97661622 + 2.96875 = 6.94536622 x = 6.94536622 Simplifying x = 6.94536622Subproblem 2
x + -2.96875 = -3.97661622 Simplifying x + -2.96875 = -3.97661622 Reorder the terms: -2.96875 + x = -3.97661622 Solving -2.96875 + x = -3.97661622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = -3.97661622 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = -3.97661622 + 2.96875 x = -3.97661622 + 2.96875 Combine like terms: -3.97661622 + 2.96875 = -1.00786622 x = -1.00786622 Simplifying x = -1.00786622Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.94536622, -1.00786622}
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