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Simplifying 2x2 + 45x + 150 = 0 Reorder the terms: 150 + 45x + 2x2 = 0 Solving 150 + 45x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 75 + 22.5x + x2 = 0 Move the constant term to the right: Add '-75' to each side of the equation. 75 + 22.5x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + 22.5x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + 22.5x + x2 = 0 + -75 22.5x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 22.5x + x2 = -75 The x term is 22.5x. Take half its coefficient (11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. 22.5x + 126.5625 + x2 = -75 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = -75 + 126.5625 Combine like terms: -75 + 126.5625 = 51.5625 126.5625 + 22.5x + x2 = 51.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 51.5625 Calculate the square root of the right side: 7.180703308 Break this problem into two subproblems by setting (x + 11.25) equal to 7.180703308 and -7.180703308.Subproblem 1
x + 11.25 = 7.180703308 Simplifying x + 11.25 = 7.180703308 Reorder the terms: 11.25 + x = 7.180703308 Solving 11.25 + x = 7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = 7.180703308 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 7.180703308 + -11.25 x = 7.180703308 + -11.25 Combine like terms: 7.180703308 + -11.25 = -4.069296692 x = -4.069296692 Simplifying x = -4.069296692Subproblem 2
x + 11.25 = -7.180703308 Simplifying x + 11.25 = -7.180703308 Reorder the terms: 11.25 + x = -7.180703308 Solving 11.25 + x = -7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = -7.180703308 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -7.180703308 + -11.25 x = -7.180703308 + -11.25 Combine like terms: -7.180703308 + -11.25 = -18.430703308 x = -18.430703308 Simplifying x = -18.430703308Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.069296692, -18.430703308}
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