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Simplifying 2x2 + 3x = 372 Reorder the terms: 3x + 2x2 = 372 Solving 3x + 2x2 = 372 Solving for variable 'x'. Reorder the terms: -372 + 3x + 2x2 = 372 + -372 Combine like terms: 372 + -372 = 0 -372 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -186 + 1.5x + x2 = 0 Move the constant term to the right: Add '186' to each side of the equation. -186 + 1.5x + 186 + x2 = 0 + 186 Reorder the terms: -186 + 186 + 1.5x + x2 = 0 + 186 Combine like terms: -186 + 186 = 0 0 + 1.5x + x2 = 0 + 186 1.5x + x2 = 0 + 186 Combine like terms: 0 + 186 = 186 1.5x + x2 = 186 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 = 186 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 186 + 0.5625 Combine like terms: 186 + 0.5625 = 186.5625 0.5625 + 1.5x + x2 = 186.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 186.5625 Calculate the square root of the right side: 13.65878838 Break this problem into two subproblems by setting (x + 0.75) equal to 13.65878838 and -13.65878838.Subproblem 1
x + 0.75 = 13.65878838 Simplifying x + 0.75 = 13.65878838 Reorder the terms: 0.75 + x = 13.65878838 Solving 0.75 + x = 13.65878838 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 = 13.65878838 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 13.65878838 + -0.75 x = 13.65878838 + -0.75 Combine like terms: 13.65878838 + -0.75 = 12.90878838 x = 12.90878838 Simplifying x = 12.90878838Subproblem 2
x + 0.75 = -13.65878838 Simplifying x + 0.75 = -13.65878838 Reorder the terms: 0.75 + x = -13.65878838 Solving 0.75 + x = -13.65878838 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 = -13.65878838 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -13.65878838 + -0.75 x = -13.65878838 + -0.75 Combine like terms: -13.65878838 + -0.75 = -14.40878838 x = -14.40878838 Simplifying x = -14.40878838Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.90878838, -14.40878838}
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