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Simplifying -16x2 + 96x + 6 = 0 Reorder the terms: 6 + 96x + -16x2 = 0 Solving 6 + 96x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 48x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 48x + -8x2)' equal to zero and attempt to solve: Simplifying 3 + 48x + -8x2 = 0 Solving 3 + 48x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -6x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -6x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -6x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -6x + x2 = 0 + 0.375 -6x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -6x + x2 = 0.375 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 = 0.375 + 9 Reorder the terms: 9 + -6x + x2 = 0.375 + 9 Combine like terms: 0.375 + 9 = 9.375 9 + -6x + x2 = 9.375 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.375 Calculate the square root of the right side: 3.061862178 Break this problem into two subproblems by setting (x + -3) equal to 3.061862178 and -3.061862178.Subproblem 1
x + -3 = 3.061862178 Simplifying x + -3 = 3.061862178 Reorder the terms: -3 + x = 3.061862178 Solving -3 + x = 3.061862178 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 = 3.061862178 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.061862178 + 3 x = 3.061862178 + 3 Combine like terms: 3.061862178 + 3 = 6.061862178 x = 6.061862178 Simplifying x = 6.061862178Subproblem 2
x + -3 = -3.061862178 Simplifying x + -3 = -3.061862178 Reorder the terms: -3 + x = -3.061862178 Solving -3 + x = -3.061862178 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 = -3.061862178 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.061862178 + 3 x = -3.061862178 + 3 Combine like terms: -3.061862178 + 3 = -0.061862178 x = -0.061862178 Simplifying x = -0.061862178Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.061862178, -0.061862178}Solution
x = {6.061862178, -0.061862178}
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