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Simplifying 2x(x + 36) = 90 Reorder the terms: 2x(36 + x) = 90 (36 * 2x + x * 2x) = 90 (72x + 2x2) = 90 Solving 72x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 72x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 72x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + 36x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + 36x + x2)' equal to zero and attempt to solve: Simplifying -45 + 36x + x2 = 0 Solving -45 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 36x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 36x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 36x + x2 = 0 + 45 36x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 36x + x2 = 45 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = 45 + 324 Reorder the terms: 324 + 36x + x2 = 45 + 324 Combine like terms: 45 + 324 = 369 324 + 36x + x2 = 369 Factor a perfect square on the left side: (x + 18)(x + 18) = 369 Calculate the square root of the right side: 19.209372712 Break this problem into two subproblems by setting (x + 18) equal to 19.209372712 and -19.209372712.Subproblem 1
x + 18 = 19.209372712 Simplifying x + 18 = 19.209372712 Reorder the terms: 18 + x = 19.209372712 Solving 18 + x = 19.209372712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 19.209372712 + -18 Combine like terms: 18 + -18 = 0 0 + x = 19.209372712 + -18 x = 19.209372712 + -18 Combine like terms: 19.209372712 + -18 = 1.209372712 x = 1.209372712 Simplifying x = 1.209372712Subproblem 2
x + 18 = -19.209372712 Simplifying x + 18 = -19.209372712 Reorder the terms: 18 + x = -19.209372712 Solving 18 + x = -19.209372712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -19.209372712 + -18 Combine like terms: 18 + -18 = 0 0 + x = -19.209372712 + -18 x = -19.209372712 + -18 Combine like terms: -19.209372712 + -18 = -37.209372712 x = -37.209372712 Simplifying x = -37.209372712Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.209372712, -37.209372712}Solution
x = {1.209372712, -37.209372712}
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