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Simplifying 2x2 + -1x = 286 Reorder the terms: -1x + 2x2 = 286 Solving -1x + 2x2 = 286 Solving for variable 'x'. Reorder the terms: -286 + -1x + 2x2 = 286 + -286 Combine like terms: 286 + -286 = 0 -286 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -143 + -0.5x + x2 = 0 Move the constant term to the right: Add '143' to each side of the equation. -143 + -0.5x + 143 + x2 = 0 + 143 Reorder the terms: -143 + 143 + -0.5x + x2 = 0 + 143 Combine like terms: -143 + 143 = 0 0 + -0.5x + x2 = 0 + 143 -0.5x + x2 = 0 + 143 Combine like terms: 0 + 143 = 143 -0.5x + x2 = 143 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 = 143 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 143 + 0.0625 Combine like terms: 143 + 0.0625 = 143.0625 0.0625 + -0.5x + x2 = 143.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 143.0625 Calculate the square root of the right side: 11.960873714 Break this problem into two subproblems by setting (x + -0.25) equal to 11.960873714 and -11.960873714.Subproblem 1
x + -0.25 = 11.960873714 Simplifying x + -0.25 = 11.960873714 Reorder the terms: -0.25 + x = 11.960873714 Solving -0.25 + x = 11.960873714 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 = 11.960873714 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 11.960873714 + 0.25 x = 11.960873714 + 0.25 Combine like terms: 11.960873714 + 0.25 = 12.210873714 x = 12.210873714 Simplifying x = 12.210873714Subproblem 2
x + -0.25 = -11.960873714 Simplifying x + -0.25 = -11.960873714 Reorder the terms: -0.25 + x = -11.960873714 Solving -0.25 + x = -11.960873714 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 = -11.960873714 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -11.960873714 + 0.25 x = -11.960873714 + 0.25 Combine like terms: -11.960873714 + 0.25 = -11.710873714 x = -11.710873714 Simplifying x = -11.710873714Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.210873714, -11.710873714}
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