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Simplifying 6x2 + 2 + -3x = 718 Reorder the terms: 2 + -3x + 6x2 = 718 Solving 2 + -3x + 6x2 = 718 Solving for variable 'x'. Reorder the terms: 2 + -718 + -3x + 6x2 = 718 + -718 Combine like terms: 2 + -718 = -716 -716 + -3x + 6x2 = 718 + -718 Combine like terms: 718 + -718 = 0 -716 + -3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -119.3333333 + -0.5x + x2 = 0 Move the constant term to the right: Add '119.3333333' to each side of the equation. -119.3333333 + -0.5x + 119.3333333 + x2 = 0 + 119.3333333 Reorder the terms: -119.3333333 + 119.3333333 + -0.5x + x2 = 0 + 119.3333333 Combine like terms: -119.3333333 + 119.3333333 = 0.0000000 0.0000000 + -0.5x + x2 = 0 + 119.3333333 -0.5x + x2 = 0 + 119.3333333 Combine like terms: 0 + 119.3333333 = 119.3333333 -0.5x + x2 = 119.3333333 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 119.3333333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 119.3333333 + 0.0625 Combine like terms: 119.3333333 + 0.0625 = 119.3958333 0.0625 + -0.5x + x2 = 119.3958333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 119.3958333 Calculate the square root of the right side: 10.926840042 Break this problem into two subproblems by setting (x + -0.25) equal to 10.926840042 and -10.926840042.Subproblem 1
x + -0.25 = 10.926840042 Simplifying x + -0.25 = 10.926840042 Reorder the terms: -0.25 + x = 10.926840042 Solving -0.25 + x = 10.926840042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 10.926840042 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 10.926840042 + 0.25 x = 10.926840042 + 0.25 Combine like terms: 10.926840042 + 0.25 = 11.176840042 x = 11.176840042 Simplifying x = 11.176840042Subproblem 2
x + -0.25 = -10.926840042 Simplifying x + -0.25 = -10.926840042 Reorder the terms: -0.25 + x = -10.926840042 Solving -0.25 + x = -10.926840042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -10.926840042 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -10.926840042 + 0.25 x = -10.926840042 + 0.25 Combine like terms: -10.926840042 + 0.25 = -10.676840042 x = -10.676840042 Simplifying x = -10.676840042Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.176840042, -10.676840042}
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