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Simplifying 18x2 + -64x + -36 = 0 Reorder the terms: -36 + -64x + 18x2 = 0 Solving -36 + -64x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -32x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + -32x + 9x2)' equal to zero and attempt to solve: Simplifying -18 + -32x + 9x2 = 0 Solving -18 + -32x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2 + -3.555555556x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -3.555555556x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -3.555555556x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3.555555556x + x2 = 0 + 2 -3.555555556x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3.555555556x + x2 = 2 The x term is -3.555555556x. Take half its coefficient (-1.777777778). Square it (3.160493828) and add it to both sides. Add '3.160493828' to each side of the equation. -3.555555556x + 3.160493828 + x2 = 2 + 3.160493828 Reorder the terms: 3.160493828 + -3.555555556x + x2 = 2 + 3.160493828 Combine like terms: 2 + 3.160493828 = 5.160493828 3.160493828 + -3.555555556x + x2 = 5.160493828 Factor a perfect square on the left side: (x + -1.777777778)(x + -1.777777778) = 5.160493828 Calculate the square root of the right side: 2.271672034 Break this problem into two subproblems by setting (x + -1.777777778) equal to 2.271672034 and -2.271672034.Subproblem 1
x + -1.777777778 = 2.271672034 Simplifying x + -1.777777778 = 2.271672034 Reorder the terms: -1.777777778 + x = 2.271672034 Solving -1.777777778 + x = 2.271672034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.777777778' to each side of the equation. -1.777777778 + 1.777777778 + x = 2.271672034 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + x = 2.271672034 + 1.777777778 x = 2.271672034 + 1.777777778 Combine like terms: 2.271672034 + 1.777777778 = 4.049449812 x = 4.049449812 Simplifying x = 4.049449812Subproblem 2
x + -1.777777778 = -2.271672034 Simplifying x + -1.777777778 = -2.271672034 Reorder the terms: -1.777777778 + x = -2.271672034 Solving -1.777777778 + x = -2.271672034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.777777778' to each side of the equation. -1.777777778 + 1.777777778 + x = -2.271672034 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + x = -2.271672034 + 1.777777778 x = -2.271672034 + 1.777777778 Combine like terms: -2.271672034 + 1.777777778 = -0.493894256 x = -0.493894256 Simplifying x = -0.493894256Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.049449812, -0.493894256}Solution
x = {4.049449812, -0.493894256}
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