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Simplifying 2x2 + x + -342 = 0 Reorder the terms: -342 + x + 2x2 = 0 Solving -342 + x + 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'. -171 + 0.5x + x2 = 0 Move the constant term to the right: Add '171' to each side of the equation. -171 + 0.5x + 171 + x2 = 0 + 171 Reorder the terms: -171 + 171 + 0.5x + x2 = 0 + 171 Combine like terms: -171 + 171 = 0 0 + 0.5x + x2 = 0 + 171 0.5x + x2 = 0 + 171 Combine like terms: 0 + 171 = 171 0.5x + x2 = 171 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 171 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 171 + 0.25 Combine like terms: 171 + 0.25 = 171.25 0.25 + 0.5x + x2 = 171.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 171.25 Calculate the square root of the right side: 13.086252328 Break this problem into two subproblems by setting (x + 0.5) equal to 13.086252328 and -13.086252328.Subproblem 1
x + 0.5 = 13.086252328 Simplifying x + 0.5 = 13.086252328 Reorder the terms: 0.5 + x = 13.086252328 Solving 0.5 + x = 13.086252328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 13.086252328 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.086252328 + -0.5 x = 13.086252328 + -0.5 Combine like terms: 13.086252328 + -0.5 = 12.586252328 x = 12.586252328 Simplifying x = 12.586252328Subproblem 2
x + 0.5 = -13.086252328 Simplifying x + 0.5 = -13.086252328 Reorder the terms: 0.5 + x = -13.086252328 Solving 0.5 + x = -13.086252328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -13.086252328 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.086252328 + -0.5 x = -13.086252328 + -0.5 Combine like terms: -13.086252328 + -0.5 = -13.586252328 x = -13.586252328 Simplifying x = -13.586252328Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.586252328, -13.586252328}
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