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Simplifying 2x2 + 3x = 150 Reorder the terms: 3x + 2x2 = 150 Solving 3x + 2x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 3x + 2x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -75 + 1.5x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 1.5x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 1.5x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 1.5x + x2 = 0 + 75 1.5x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 1.5x + x2 = 75 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 = 75 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 75 + 0.5625 Combine like terms: 75 + 0.5625 = 75.5625 0.5625 + 1.5x + x2 = 75.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 75.5625 Calculate the square root of the right side: 8.692669325 Break this problem into two subproblems by setting (x + 0.75) equal to 8.692669325 and -8.692669325.Subproblem 1
x + 0.75 = 8.692669325 Simplifying x + 0.75 = 8.692669325 Reorder the terms: 0.75 + x = 8.692669325 Solving 0.75 + x = 8.692669325 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 = 8.692669325 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 8.692669325 + -0.75 x = 8.692669325 + -0.75 Combine like terms: 8.692669325 + -0.75 = 7.942669325 x = 7.942669325 Simplifying x = 7.942669325Subproblem 2
x + 0.75 = -8.692669325 Simplifying x + 0.75 = -8.692669325 Reorder the terms: 0.75 + x = -8.692669325 Solving 0.75 + x = -8.692669325 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 = -8.692669325 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -8.692669325 + -0.75 x = -8.692669325 + -0.75 Combine like terms: -8.692669325 + -0.75 = -9.442669325 x = -9.442669325 Simplifying x = -9.442669325Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.942669325, -9.442669325}
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