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Simplifying 6x2 + -9x + -52 = 0 Reorder the terms: -52 + -9x + 6x2 = 0 Solving -52 + -9x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -8.666666667 + -1.5x + x2 = 0 Move the constant term to the right: Add '8.666666667' to each side of the equation. -8.666666667 + -1.5x + 8.666666667 + x2 = 0 + 8.666666667 Reorder the terms: -8.666666667 + 8.666666667 + -1.5x + x2 = 0 + 8.666666667 Combine like terms: -8.666666667 + 8.666666667 = 0.000000000 0.000000000 + -1.5x + x2 = 0 + 8.666666667 -1.5x + x2 = 0 + 8.666666667 Combine like terms: 0 + 8.666666667 = 8.666666667 -1.5x + x2 = 8.666666667 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 = 8.666666667 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 8.666666667 + 0.5625 Combine like terms: 8.666666667 + 0.5625 = 9.229166667 0.5625 + -1.5x + x2 = 9.229166667 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 9.229166667 Calculate the square root of the right side: 3.037954356 Break this problem into two subproblems by setting (x + -0.75) equal to 3.037954356 and -3.037954356.Subproblem 1
x + -0.75 = 3.037954356 Simplifying x + -0.75 = 3.037954356 Reorder the terms: -0.75 + x = 3.037954356 Solving -0.75 + x = 3.037954356 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 = 3.037954356 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.037954356 + 0.75 x = 3.037954356 + 0.75 Combine like terms: 3.037954356 + 0.75 = 3.787954356 x = 3.787954356 Simplifying x = 3.787954356Subproblem 2
x + -0.75 = -3.037954356 Simplifying x + -0.75 = -3.037954356 Reorder the terms: -0.75 + x = -3.037954356 Solving -0.75 + x = -3.037954356 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 = -3.037954356 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.037954356 + 0.75 x = -3.037954356 + 0.75 Combine like terms: -3.037954356 + 0.75 = -2.287954356 x = -2.287954356 Simplifying x = -2.287954356Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.787954356, -2.287954356}
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