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Simplifying -16x2 + 48x + 432 = 0 Reorder the terms: 432 + 48x + -16x2 = 0 Solving 432 + 48x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(27 + 3x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(27 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying 27 + 3x + -1x2 = 0 Solving 27 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -27 + -3x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -3x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -3x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -3x + x2 = 0 + 27 -3x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -3x + x2 = 27 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 = 27 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 27 + 2.25 Combine like terms: 27 + 2.25 = 29.25 2.25 + -3x + x2 = 29.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + -1.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + -1.5 = 5.408326913 Simplifying x + -1.5 = 5.408326913 Reorder the terms: -1.5 + x = 5.408326913 Solving -1.5 + x = 5.408326913 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 = 5.408326913 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.408326913 + 1.5 x = 5.408326913 + 1.5 Combine like terms: 5.408326913 + 1.5 = 6.908326913 x = 6.908326913 Simplifying x = 6.908326913Subproblem 2
x + -1.5 = -5.408326913 Simplifying x + -1.5 = -5.408326913 Reorder the terms: -1.5 + x = -5.408326913 Solving -1.5 + x = -5.408326913 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 = -5.408326913 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.408326913 + 1.5 x = -5.408326913 + 1.5 Combine like terms: -5.408326913 + 1.5 = -3.908326913 x = -3.908326913 Simplifying x = -3.908326913Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.908326913, -3.908326913}Solution
x = {6.908326913, -3.908326913}
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