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Simplifying -16x2 + 144x + 144 = 0 Reorder the terms: 144 + 144x + -16x2 = 0 Solving 144 + 144x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(9 + 9x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(9 + 9x + -1x2)' equal to zero and attempt to solve: Simplifying 9 + 9x + -1x2 = 0 Solving 9 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -9x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -9x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -9x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -9x + x2 = 0 + 9 -9x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -9x + x2 = 9 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 9 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 9 + 20.25 Combine like terms: 9 + 20.25 = 29.25 20.25 + -9x + x2 = 29.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + -4.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + -4.5 = 5.408326913 Simplifying x + -4.5 = 5.408326913 Reorder the terms: -4.5 + x = 5.408326913 Solving -4.5 + x = 5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.408326913 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.408326913 + 4.5 x = 5.408326913 + 4.5 Combine like terms: 5.408326913 + 4.5 = 9.908326913 x = 9.908326913 Simplifying x = 9.908326913Subproblem 2
x + -4.5 = -5.408326913 Simplifying x + -4.5 = -5.408326913 Reorder the terms: -4.5 + x = -5.408326913 Solving -4.5 + x = -5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.408326913 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.408326913 + 4.5 x = -5.408326913 + 4.5 Combine like terms: -5.408326913 + 4.5 = -0.908326913 x = -0.908326913 Simplifying x = -0.908326913Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.908326913, -0.908326913}Solution
x = {9.908326913, -0.908326913}
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