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Simplifying 36x2 + -162x + -180 = 0 Reorder the terms: -180 + -162x + 36x2 = 0 Solving -180 + -162x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '18'. 18(-10 + -9x + 2x2) = 0 Ignore the factor 18.Subproblem 1
Set the factor '(-10 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying -10 + -9x + 2x2 = 0 Solving -10 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + -4.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -4.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.5x + x2 = 0 + 5 -4.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4.5x + x2 = 5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 5 + 5.0625 Combine like terms: 5 + 5.0625 = 10.0625 5.0625 + -4.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + -2.25) equal to 3.172144385 and -3.172144385.Subproblem 1
x + -2.25 = 3.172144385 Simplifying x + -2.25 = 3.172144385 Reorder the terms: -2.25 + x = 3.172144385 Solving -2.25 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 3.172144385 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 3.172144385 + 2.25 x = 3.172144385 + 2.25 Combine like terms: 3.172144385 + 2.25 = 5.422144385 x = 5.422144385 Simplifying x = 5.422144385Subproblem 2
x + -2.25 = -3.172144385 Simplifying x + -2.25 = -3.172144385 Reorder the terms: -2.25 + x = -3.172144385 Solving -2.25 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -3.172144385 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -3.172144385 + 2.25 x = -3.172144385 + 2.25 Combine like terms: -3.172144385 + 2.25 = -0.922144385 x = -0.922144385 Simplifying x = -0.922144385Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.422144385, -0.922144385}Solution
x = {5.422144385, -0.922144385}
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