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Simplifying 16x2 + 48x + -66 = 0 Reorder the terms: -66 + 48x + 16x2 = 0 Solving -66 + 48x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + 24x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-33 + 24x + 8x2)' equal to zero and attempt to solve: Simplifying -33 + 24x + 8x2 = 0 Solving -33 + 24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.125 + 3x + x2 = 0 Move the constant term to the right: Add '4.125' to each side of the equation. -4.125 + 3x + 4.125 + x2 = 0 + 4.125 Reorder the terms: -4.125 + 4.125 + 3x + x2 = 0 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + 3x + x2 = 0 + 4.125 3x + x2 = 0 + 4.125 Combine like terms: 0 + 4.125 = 4.125 3x + x2 = 4.125 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 4.125 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 4.125 + 2.25 Combine like terms: 4.125 + 2.25 = 6.375 2.25 + 3x + x2 = 6.375 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 6.375 Calculate the square root of the right side: 2.524876235 Break this problem into two subproblems by setting (x + 1.5) equal to 2.524876235 and -2.524876235.Subproblem 1
x + 1.5 = 2.524876235 Simplifying x + 1.5 = 2.524876235 Reorder the terms: 1.5 + x = 2.524876235 Solving 1.5 + x = 2.524876235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.524876235 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.524876235 + -1.5 x = 2.524876235 + -1.5 Combine like terms: 2.524876235 + -1.5 = 1.024876235 x = 1.024876235 Simplifying x = 1.024876235Subproblem 2
x + 1.5 = -2.524876235 Simplifying x + 1.5 = -2.524876235 Reorder the terms: 1.5 + x = -2.524876235 Solving 1.5 + x = -2.524876235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.524876235 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.524876235 + -1.5 x = -2.524876235 + -1.5 Combine like terms: -2.524876235 + -1.5 = -4.024876235 x = -4.024876235 Simplifying x = -4.024876235Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.024876235, -4.024876235}Solution
x = {1.024876235, -4.024876235}
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