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Simplifying 0 = -16x2 + 96x + 408 Reorder the terms: 0 = 408 + 96x + -16x2 Solving 0 = 408 + 96x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -408 = -408 -408 + -96x + 16x2 = 408 + 96x + -16x2 + -408 + -96x + 16x2 Reorder the terms: -408 + -96x + 16x2 = 408 + -408 + 96x + -96x + -16x2 + 16x2 Combine like terms: 408 + -408 = 0 -408 + -96x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2 -408 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 -408 + -96x + 16x2 = 0 + -16x2 + 16x2 -408 + -96x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -408 + -96x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-51 + -12x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-51 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying -51 + -12x + 2x2 = 0 Solving -51 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25.5 + -6x + x2 = 0 Move the constant term to the right: Add '25.5' to each side of the equation. -25.5 + -6x + 25.5 + x2 = 0 + 25.5 Reorder the terms: -25.5 + 25.5 + -6x + x2 = 0 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + -6x + x2 = 0 + 25.5 -6x + x2 = 0 + 25.5 Combine like terms: 0 + 25.5 = 25.5 -6x + x2 = 25.5 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 = 25.5 + 9 Reorder the terms: 9 + -6x + x2 = 25.5 + 9 Combine like terms: 25.5 + 9 = 34.5 9 + -6x + x2 = 34.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 34.5 Calculate the square root of the right side: 5.873670062 Break this problem into two subproblems by setting (x + -3) equal to 5.873670062 and -5.873670062.Subproblem 1
x + -3 = 5.873670062 Simplifying x + -3 = 5.873670062 Reorder the terms: -3 + x = 5.873670062 Solving -3 + x = 5.873670062 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 = 5.873670062 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.873670062 + 3 x = 5.873670062 + 3 Combine like terms: 5.873670062 + 3 = 8.873670062 x = 8.873670062 Simplifying x = 8.873670062Subproblem 2
x + -3 = -5.873670062 Simplifying x + -3 = -5.873670062 Reorder the terms: -3 + x = -5.873670062 Solving -3 + x = -5.873670062 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 = -5.873670062 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.873670062 + 3 x = -5.873670062 + 3 Combine like terms: -5.873670062 + 3 = -2.873670062 x = -2.873670062 Simplifying x = -2.873670062Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.873670062, -2.873670062}Solution
x = {8.873670062, -2.873670062}
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