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Simplifying -16x2 + 144x + 288 = 0 Reorder the terms: 288 + 144x + -16x2 = 0 Solving 288 + 144x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(18 + 9x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(18 + 9x + -1x2)' equal to zero and attempt to solve: Simplifying 18 + 9x + -1x2 = 0 Solving 18 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + -9x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -9x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -9x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -9x + x2 = 0 + 18 -9x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -9x + x2 = 18 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 = 18 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 18 + 20.25 Combine like terms: 18 + 20.25 = 38.25 20.25 + -9x + x2 = 38.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + -4.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + -4.5 = 6.184658438 Simplifying x + -4.5 = 6.184658438 Reorder the terms: -4.5 + x = 6.184658438 Solving -4.5 + x = 6.184658438 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 = 6.184658438 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.184658438 + 4.5 x = 6.184658438 + 4.5 Combine like terms: 6.184658438 + 4.5 = 10.684658438 x = 10.684658438 Simplifying x = 10.684658438Subproblem 2
x + -4.5 = -6.184658438 Simplifying x + -4.5 = -6.184658438 Reorder the terms: -4.5 + x = -6.184658438 Solving -4.5 + x = -6.184658438 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 = -6.184658438 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.184658438 + 4.5 x = -6.184658438 + 4.5 Combine like terms: -6.184658438 + 4.5 = -1.684658438 x = -1.684658438 Simplifying x = -1.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.684658438, -1.684658438}Solution
x = {10.684658438, -1.684658438}
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