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Simplifying 0 = -16x2 + 96x + 140 Reorder the terms: 0 = 140 + 96x + -16x2 Solving 0 = 140 + 96x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -140 = -140 -140 + -96x + 16x2 = 140 + 96x + -16x2 + -140 + -96x + 16x2 Reorder the terms: -140 + -96x + 16x2 = 140 + -140 + 96x + -96x + -16x2 + 16x2 Combine like terms: 140 + -140 = 0 -140 + -96x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2 -140 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 -140 + -96x + 16x2 = 0 + -16x2 + 16x2 -140 + -96x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -140 + -96x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-35 + -24x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-35 + -24x + 4x2)' equal to zero and attempt to solve: Simplifying -35 + -24x + 4x2 = 0 Solving -35 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + -6x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -6x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -6x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -6x + x2 = 0 + 8.75 -6x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -6x + x2 = 8.75 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 8.75 + 9 Reorder the terms: 9 + -6x + x2 = 8.75 + 9 Combine like terms: 8.75 + 9 = 17.75 9 + -6x + x2 = 17.75 Factor a perfect square on the left side: (x + -3)(x + -3) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (x + -3) equal to 4.213074887 and -4.213074887.Subproblem 1
x + -3 = 4.213074887 Simplifying x + -3 = 4.213074887 Reorder the terms: -3 + x = 4.213074887 Solving -3 + x = 4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.213074887 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.213074887 + 3 x = 4.213074887 + 3 Combine like terms: 4.213074887 + 3 = 7.213074887 x = 7.213074887 Simplifying x = 7.213074887Subproblem 2
x + -3 = -4.213074887 Simplifying x + -3 = -4.213074887 Reorder the terms: -3 + x = -4.213074887 Solving -3 + x = -4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.213074887 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.213074887 + 3 x = -4.213074887 + 3 Combine like terms: -4.213074887 + 3 = -1.213074887 x = -1.213074887 Simplifying x = -1.213074887Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.213074887, -1.213074887}Solution
x = {7.213074887, -1.213074887}
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