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Simplifying -16x2 + 96x + 4 = 128 Reorder the terms: 4 + 96x + -16x2 = 128 Solving 4 + 96x + -16x2 = 128 Solving for variable 'x'. Reorder the terms: 4 + -128 + 96x + -16x2 = 128 + -128 Combine like terms: 4 + -128 = -124 -124 + 96x + -16x2 = 128 + -128 Combine like terms: 128 + -128 = 0 -124 + 96x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-31 + 24x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-31 + 24x + -4x2)' equal to zero and attempt to solve: Simplifying -31 + 24x + -4x2 = 0 Solving -31 + 24x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 7.75 + -6x + x2 = 0 Move the constant term to the right: Add '-7.75' to each side of the equation. 7.75 + -6x + -7.75 + x2 = 0 + -7.75 Reorder the terms: 7.75 + -7.75 + -6x + x2 = 0 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + -6x + x2 = 0 + -7.75 -6x + x2 = 0 + -7.75 Combine like terms: 0 + -7.75 = -7.75 -6x + x2 = -7.75 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 = -7.75 + 9 Reorder the terms: 9 + -6x + x2 = -7.75 + 9 Combine like terms: -7.75 + 9 = 1.25 9 + -6x + x2 = 1.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -3) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -3 = 1.118033989 Simplifying x + -3 = 1.118033989 Reorder the terms: -3 + x = 1.118033989 Solving -3 + x = 1.118033989 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 = 1.118033989 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.118033989 + 3 x = 1.118033989 + 3 Combine like terms: 1.118033989 + 3 = 4.118033989 x = 4.118033989 Simplifying x = 4.118033989Subproblem 2
x + -3 = -1.118033989 Simplifying x + -3 = -1.118033989 Reorder the terms: -3 + x = -1.118033989 Solving -3 + x = -1.118033989 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 = -1.118033989 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.118033989 + 3 x = -1.118033989 + 3 Combine like terms: -1.118033989 + 3 = 1.881966011 x = 1.881966011 Simplifying x = 1.881966011Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.118033989, 1.881966011}Solution
x = {4.118033989, 1.881966011}
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