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Simplifying 0 = -16x2 + 96x + 110 Reorder the terms: 0 = 110 + 96x + -16x2 Solving 0 = 110 + 96x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -110 = -110 -110 + -96x + 16x2 = 110 + 96x + -16x2 + -110 + -96x + 16x2 Reorder the terms: -110 + -96x + 16x2 = 110 + -110 + 96x + -96x + -16x2 + 16x2 Combine like terms: 110 + -110 = 0 -110 + -96x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2 -110 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 -110 + -96x + 16x2 = 0 + -16x2 + 16x2 -110 + -96x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -110 + -96x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + -48x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-55 + -48x + 8x2)' equal to zero and attempt to solve: Simplifying -55 + -48x + 8x2 = 0 Solving -55 + -48x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.875 + -6x + x2 = 0 Move the constant term to the right: Add '6.875' to each side of the equation. -6.875 + -6x + 6.875 + x2 = 0 + 6.875 Reorder the terms: -6.875 + 6.875 + -6x + x2 = 0 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + -6x + x2 = 0 + 6.875 -6x + x2 = 0 + 6.875 Combine like terms: 0 + 6.875 = 6.875 -6x + x2 = 6.875 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 = 6.875 + 9 Reorder the terms: 9 + -6x + x2 = 6.875 + 9 Combine like terms: 6.875 + 9 = 15.875 9 + -6x + x2 = 15.875 Factor a perfect square on the left side: (x + -3)(x + -3) = 15.875 Calculate the square root of the right side: 3.984344363 Break this problem into two subproblems by setting (x + -3) equal to 3.984344363 and -3.984344363.Subproblem 1
x + -3 = 3.984344363 Simplifying x + -3 = 3.984344363 Reorder the terms: -3 + x = 3.984344363 Solving -3 + x = 3.984344363 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 = 3.984344363 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.984344363 + 3 x = 3.984344363 + 3 Combine like terms: 3.984344363 + 3 = 6.984344363 x = 6.984344363 Simplifying x = 6.984344363Subproblem 2
x + -3 = -3.984344363 Simplifying x + -3 = -3.984344363 Reorder the terms: -3 + x = -3.984344363 Solving -3 + x = -3.984344363 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 = -3.984344363 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.984344363 + 3 x = -3.984344363 + 3 Combine like terms: -3.984344363 + 3 = -0.984344363 x = -0.984344363 Simplifying x = -0.984344363Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.984344363, -0.984344363}Solution
x = {6.984344363, -0.984344363}
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