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Simplifying 0 = -16x2 + 96x + 4 Reorder the terms: 0 = 4 + 96x + -16x2 Solving 0 = 4 + 96x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -96x + 16x2 = 4 + 96x + -16x2 + -4 + -96x + 16x2 Reorder the terms: -4 + -96x + 16x2 = 4 + -4 + 96x + -96x + -16x2 + 16x2 Combine like terms: 4 + -4 = 0 -4 + -96x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2 -4 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 -4 + -96x + 16x2 = 0 + -16x2 + 16x2 -4 + -96x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -4 + -96x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -24x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -24x + 4x2)' equal to zero and attempt to solve: Simplifying -1 + -24x + 4x2 = 0 Solving -1 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -6x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -6x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -6x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -6x + x2 = 0 + 0.25 -6x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -6x + x2 = 0.25 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 = 0.25 + 9 Reorder the terms: 9 + -6x + x2 = 0.25 + 9 Combine like terms: 0.25 + 9 = 9.25 9 + -6x + x2 = 9.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + -3) equal to 3.041381265 and -3.041381265.Subproblem 1
x + -3 = 3.041381265 Simplifying x + -3 = 3.041381265 Reorder the terms: -3 + x = 3.041381265 Solving -3 + x = 3.041381265 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 = 3.041381265 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.041381265 + 3 x = 3.041381265 + 3 Combine like terms: 3.041381265 + 3 = 6.041381265 x = 6.041381265 Simplifying x = 6.041381265Subproblem 2
x + -3 = -3.041381265 Simplifying x + -3 = -3.041381265 Reorder the terms: -3 + x = -3.041381265 Solving -3 + x = -3.041381265 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 = -3.041381265 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.041381265 + 3 x = -3.041381265 + 3 Combine like terms: -3.041381265 + 3 = -0.041381265 x = -0.041381265 Simplifying x = -0.041381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.041381265, -0.041381265}Solution
x = {6.041381265, -0.041381265}
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