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Simplifying 0 = 150x + 15x + 20 + 2x2 Reorder the terms: 0 = 20 + 150x + 15x + 2x2 Combine like terms: 150x + 15x = 165x 0 = 20 + 165x + 2x2 Solving 0 = 20 + 165x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -165x + -2x2 = 20 + 165x + 2x2 + -20 + -165x + -2x2 Reorder the terms: -20 + -165x + -2x2 = 20 + -20 + 165x + -165x + 2x2 + -2x2 Combine like terms: 20 + -20 = 0 -20 + -165x + -2x2 = 0 + 165x + -165x + 2x2 + -2x2 -20 + -165x + -2x2 = 165x + -165x + 2x2 + -2x2 Combine like terms: 165x + -165x = 0 -20 + -165x + -2x2 = 0 + 2x2 + -2x2 -20 + -165x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -20 + -165x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 165x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(20 + 165x + 2x2)' equal to zero and attempt to solve: Simplifying 20 + 165x + 2x2 = 0 Solving 20 + 165x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10 + 82.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 82.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 82.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 82.5x + x2 = 0 + -10 82.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 82.5x + x2 = -10 The x term is 82.5x. Take half its coefficient (41.25). Square it (1701.5625) and add it to both sides. Add '1701.5625' to each side of the equation. 82.5x + 1701.5625 + x2 = -10 + 1701.5625 Reorder the terms: 1701.5625 + 82.5x + x2 = -10 + 1701.5625 Combine like terms: -10 + 1701.5625 = 1691.5625 1701.5625 + 82.5x + x2 = 1691.5625 Factor a perfect square on the left side: (x + 41.25)(x + 41.25) = 1691.5625 Calculate the square root of the right side: 41.128609264 Break this problem into two subproblems by setting (x + 41.25) equal to 41.128609264 and -41.128609264.Subproblem 1
x + 41.25 = 41.128609264 Simplifying x + 41.25 = 41.128609264 Reorder the terms: 41.25 + x = 41.128609264 Solving 41.25 + x = 41.128609264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-41.25' to each side of the equation. 41.25 + -41.25 + x = 41.128609264 + -41.25 Combine like terms: 41.25 + -41.25 = 0.00 0.00 + x = 41.128609264 + -41.25 x = 41.128609264 + -41.25 Combine like terms: 41.128609264 + -41.25 = -0.121390736 x = -0.121390736 Simplifying x = -0.121390736Subproblem 2
x + 41.25 = -41.128609264 Simplifying x + 41.25 = -41.128609264 Reorder the terms: 41.25 + x = -41.128609264 Solving 41.25 + x = -41.128609264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-41.25' to each side of the equation. 41.25 + -41.25 + x = -41.128609264 + -41.25 Combine like terms: 41.25 + -41.25 = 0.00 0.00 + x = -41.128609264 + -41.25 x = -41.128609264 + -41.25 Combine like terms: -41.128609264 + -41.25 = -82.378609264 x = -82.378609264 Simplifying x = -82.378609264Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.121390736, -82.378609264}Solution
x = {-0.121390736, -82.378609264}
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