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Simplifying 0 = (16x2) + 144x + -288 Reorder the terms: 0 = -288 + 144x + (16x2) Solving 0 = -288 + 144x + (16x2) Solving for variable 'x'. Combine like terms: 0 + 288 = 288 288 + -144x + (-16x2) = -288 + 144x + (16x2) + 288 + -144x + (-16x2) Reorder the terms: 288 + -144x + (-16x2) = -288 + 288 + 144x + -144x + (16x2) + (-16x2) Combine like terms: -288 + 288 = 0 288 + -144x + (-16x2) = 0 + 144x + -144x + (16x2) + (-16x2) 288 + -144x + (-16x2) = 144x + -144x + (16x2) + (-16x2) Combine like terms: 144x + -144x = 0 288 + -144x + (-16x2) = 0 + (16x2) + (-16x2) 288 + -144x + (-16x2) = (16x2) + (-16x2) Combine like terms: (16x2) + (-16x2) = 0 288 + -144x + (-16x2) = 0 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 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 = 1.684658438Subproblem 2
(x) + 4.5 = -6.184658438 Simplifying (x) + 4.5 = -6.184658438 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 = -10.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.684658438, -10.684658438}Solution
x = {1.684658438, -10.684658438}
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