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Simplifying 2x2 + -3x + -117 = 0 Reorder the terms: -117 + -3x + 2x2 = 0 Solving -117 + -3x + 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'. -58.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '58.5' to each side of the equation. -58.5 + -1.5x + 58.5 + x2 = 0 + 58.5 Reorder the terms: -58.5 + 58.5 + -1.5x + x2 = 0 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + -1.5x + x2 = 0 + 58.5 -1.5x + x2 = 0 + 58.5 Combine like terms: 0 + 58.5 = 58.5 -1.5x + x2 = 58.5 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 = 58.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 58.5 + 0.5625 Combine like terms: 58.5 + 0.5625 = 59.0625 0.5625 + -1.5x + x2 = 59.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 59.0625 Calculate the square root of the right side: 7.685213074 Break this problem into two subproblems by setting (x + -0.75) equal to 7.685213074 and -7.685213074.Subproblem 1
x + -0.75 = 7.685213074 Simplifying x + -0.75 = 7.685213074 Reorder the terms: -0.75 + x = 7.685213074 Solving -0.75 + x = 7.685213074 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 = 7.685213074 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 7.685213074 + 0.75 x = 7.685213074 + 0.75 Combine like terms: 7.685213074 + 0.75 = 8.435213074 x = 8.435213074 Simplifying x = 8.435213074Subproblem 2
x + -0.75 = -7.685213074 Simplifying x + -0.75 = -7.685213074 Reorder the terms: -0.75 + x = -7.685213074 Solving -0.75 + x = -7.685213074 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 = -7.685213074 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -7.685213074 + 0.75 x = -7.685213074 + 0.75 Combine like terms: -7.685213074 + 0.75 = -6.935213074 x = -6.935213074 Simplifying x = -6.935213074Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.435213074, -6.935213074}
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