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Simplifying 2x2 + x + 15 + 2x + -10 = 180 Reorder the terms: 15 + -10 + x + 2x + 2x2 = 180 Combine like terms: 15 + -10 = 5 5 + x + 2x + 2x2 = 180 Combine like terms: x + 2x = 3x 5 + 3x + 2x2 = 180 Solving 5 + 3x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 5 + -180 + 3x + 2x2 = 180 + -180 Combine like terms: 5 + -180 = -175 -175 + 3x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -175 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -87.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '87.5' to each side of the equation. -87.5 + 1.5x + 87.5 + x2 = 0 + 87.5 Reorder the terms: -87.5 + 87.5 + 1.5x + x2 = 0 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + 1.5x + x2 = 0 + 87.5 1.5x + x2 = 0 + 87.5 Combine like terms: 0 + 87.5 = 87.5 1.5x + x2 = 87.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 87.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 87.5 + 0.5625 Combine like terms: 87.5 + 0.5625 = 88.0625 0.5625 + 1.5x + x2 = 88.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 88.0625 Calculate the square root of the right side: 9.38416219 Break this problem into two subproblems by setting (x + 0.75) equal to 9.38416219 and -9.38416219.Subproblem 1
x + 0.75 = 9.38416219 Simplifying x + 0.75 = 9.38416219 Reorder the terms: 0.75 + x = 9.38416219 Solving 0.75 + x = 9.38416219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 9.38416219 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 9.38416219 + -0.75 x = 9.38416219 + -0.75 Combine like terms: 9.38416219 + -0.75 = 8.63416219 x = 8.63416219 Simplifying x = 8.63416219Subproblem 2
x + 0.75 = -9.38416219 Simplifying x + 0.75 = -9.38416219 Reorder the terms: 0.75 + x = -9.38416219 Solving 0.75 + x = -9.38416219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -9.38416219 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -9.38416219 + -0.75 x = -9.38416219 + -0.75 Combine like terms: -9.38416219 + -0.75 = -10.13416219 x = -10.13416219 Simplifying x = -10.13416219Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.63416219, -10.13416219}
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