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Simplifying 4x2 + -66x + 180 = 0 Reorder the terms: 180 + -66x + 4x2 = 0 Solving 180 + -66x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -33x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(90 + -33x + 2x2)' equal to zero and attempt to solve: Simplifying 90 + -33x + 2x2 = 0 Solving 90 + -33x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 45 + -16.5x + x2 = 0 Move the constant term to the right: Add '-45' to each side of the equation. 45 + -16.5x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -16.5x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -16.5x + x2 = 0 + -45 -16.5x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -16.5x + x2 = -45 The x term is -16.5x. Take half its coefficient (-8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. -16.5x + 68.0625 + x2 = -45 + 68.0625 Reorder the terms: 68.0625 + -16.5x + x2 = -45 + 68.0625 Combine like terms: -45 + 68.0625 = 23.0625 68.0625 + -16.5x + x2 = 23.0625 Factor a perfect square on the left side: (x + -8.25)(x + -8.25) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x + -8.25) equal to 4.802343178 and -4.802343178.Subproblem 1
x + -8.25 = 4.802343178 Simplifying x + -8.25 = 4.802343178 Reorder the terms: -8.25 + x = 4.802343178 Solving -8.25 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = 4.802343178 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = 4.802343178 + 8.25 x = 4.802343178 + 8.25 Combine like terms: 4.802343178 + 8.25 = 13.052343178 x = 13.052343178 Simplifying x = 13.052343178Subproblem 2
x + -8.25 = -4.802343178 Simplifying x + -8.25 = -4.802343178 Reorder the terms: -8.25 + x = -4.802343178 Solving -8.25 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = -4.802343178 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = -4.802343178 + 8.25 x = -4.802343178 + 8.25 Combine like terms: -4.802343178 + 8.25 = 3.447656822 x = 3.447656822 Simplifying x = 3.447656822Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.052343178, 3.447656822}Solution
x = {13.052343178, 3.447656822}
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