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Simplifying 36x2 + -8x + -122 = 0 Reorder the terms: -122 + -8x + 36x2 = 0 Solving -122 + -8x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-61 + -4x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-61 + -4x + 18x2)' equal to zero and attempt to solve: Simplifying -61 + -4x + 18x2 = 0 Solving -61 + -4x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -3.388888889 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '3.388888889' to each side of the equation. -3.388888889 + -0.2222222222x + 3.388888889 + x2 = 0 + 3.388888889 Reorder the terms: -3.388888889 + 3.388888889 + -0.2222222222x + x2 = 0 + 3.388888889 Combine like terms: -3.388888889 + 3.388888889 = 0.000000000 0.000000000 + -0.2222222222x + x2 = 0 + 3.388888889 -0.2222222222x + x2 = 0 + 3.388888889 Combine like terms: 0 + 3.388888889 = 3.388888889 -0.2222222222x + x2 = 3.388888889 The x term is -0.2222222222x. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x + 0.01234567901 + x2 = 3.388888889 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 3.388888889 + 0.01234567901 Combine like terms: 3.388888889 + 0.01234567901 = 3.40123456801 0.01234567901 + -0.2222222222x + x2 = 3.40123456801 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 3.40123456801 Calculate the square root of the right side: 1.84424363 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 1.84424363 and -1.84424363.Subproblem 1
x + -0.1111111111 = 1.84424363 Simplifying x + -0.1111111111 = 1.84424363 Reorder the terms: -0.1111111111 + x = 1.84424363 Solving -0.1111111111 + x = 1.84424363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = 1.84424363 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 1.84424363 + 0.1111111111 x = 1.84424363 + 0.1111111111 Combine like terms: 1.84424363 + 0.1111111111 = 1.9553547411 x = 1.9553547411 Simplifying x = 1.9553547411Subproblem 2
x + -0.1111111111 = -1.84424363 Simplifying x + -0.1111111111 = -1.84424363 Reorder the terms: -0.1111111111 + x = -1.84424363 Solving -0.1111111111 + x = -1.84424363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = -1.84424363 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -1.84424363 + 0.1111111111 x = -1.84424363 + 0.1111111111 Combine like terms: -1.84424363 + 0.1111111111 = -1.7331325189 x = -1.7331325189 Simplifying x = -1.7331325189Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9553547411, -1.7331325189}Solution
x = {1.9553547411, -1.7331325189}
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