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Simplifying 36x2 + -146x + 118 = 0 Reorder the terms: 118 + -146x + 36x2 = 0 Solving 118 + -146x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(59 + -73x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(59 + -73x + 18x2)' equal to zero and attempt to solve: Simplifying 59 + -73x + 18x2 = 0 Solving 59 + -73x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 3.277777778 + -4.055555556x + x2 = 0 Move the constant term to the right: Add '-3.277777778' to each side of the equation. 3.277777778 + -4.055555556x + -3.277777778 + x2 = 0 + -3.277777778 Reorder the terms: 3.277777778 + -3.277777778 + -4.055555556x + x2 = 0 + -3.277777778 Combine like terms: 3.277777778 + -3.277777778 = 0.000000000 0.000000000 + -4.055555556x + x2 = 0 + -3.277777778 -4.055555556x + x2 = 0 + -3.277777778 Combine like terms: 0 + -3.277777778 = -3.277777778 -4.055555556x + x2 = -3.277777778 The x term is -4.055555556x. Take half its coefficient (-2.027777778). Square it (4.111882717) and add it to both sides. Add '4.111882717' to each side of the equation. -4.055555556x + 4.111882717 + x2 = -3.277777778 + 4.111882717 Reorder the terms: 4.111882717 + -4.055555556x + x2 = -3.277777778 + 4.111882717 Combine like terms: -3.277777778 + 4.111882717 = 0.834104939 4.111882717 + -4.055555556x + x2 = 0.834104939 Factor a perfect square on the left side: (x + -2.027777778)(x + -2.027777778) = 0.834104939 Calculate the square root of the right side: 0.913293457 Break this problem into two subproblems by setting (x + -2.027777778) equal to 0.913293457 and -0.913293457.Subproblem 1
x + -2.027777778 = 0.913293457 Simplifying x + -2.027777778 = 0.913293457 Reorder the terms: -2.027777778 + x = 0.913293457 Solving -2.027777778 + x = 0.913293457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.027777778' to each side of the equation. -2.027777778 + 2.027777778 + x = 0.913293457 + 2.027777778 Combine like terms: -2.027777778 + 2.027777778 = 0.000000000 0.000000000 + x = 0.913293457 + 2.027777778 x = 0.913293457 + 2.027777778 Combine like terms: 0.913293457 + 2.027777778 = 2.941071235 x = 2.941071235 Simplifying x = 2.941071235Subproblem 2
x + -2.027777778 = -0.913293457 Simplifying x + -2.027777778 = -0.913293457 Reorder the terms: -2.027777778 + x = -0.913293457 Solving -2.027777778 + x = -0.913293457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.027777778' to each side of the equation. -2.027777778 + 2.027777778 + x = -0.913293457 + 2.027777778 Combine like terms: -2.027777778 + 2.027777778 = 0.000000000 0.000000000 + x = -0.913293457 + 2.027777778 x = -0.913293457 + 2.027777778 Combine like terms: -0.913293457 + 2.027777778 = 1.114484321 x = 1.114484321 Simplifying x = 1.114484321Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.941071235, 1.114484321}Solution
x = {2.941071235, 1.114484321}
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