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Simplifying 2x2 + -31x + 12 = 0 Reorder the terms: 12 + -31x + 2x2 = 0 Solving 12 + -31x + 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'. 6 + -15.5x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -15.5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -15.5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -15.5x + x2 = 0 + -6 -15.5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -15.5x + x2 = -6 The x term is -15.5x. Take half its coefficient (-7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. -15.5x + 60.0625 + x2 = -6 + 60.0625 Reorder the terms: 60.0625 + -15.5x + x2 = -6 + 60.0625 Combine like terms: -6 + 60.0625 = 54.0625 60.0625 + -15.5x + x2 = 54.0625 Factor a perfect square on the left side: (x + -7.75)(x + -7.75) = 54.0625 Calculate the square root of the right side: 7.352720585 Break this problem into two subproblems by setting (x + -7.75) equal to 7.352720585 and -7.352720585.Subproblem 1
x + -7.75 = 7.352720585 Simplifying x + -7.75 = 7.352720585 Reorder the terms: -7.75 + x = 7.352720585 Solving -7.75 + x = 7.352720585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = 7.352720585 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = 7.352720585 + 7.75 x = 7.352720585 + 7.75 Combine like terms: 7.352720585 + 7.75 = 15.102720585 x = 15.102720585 Simplifying x = 15.102720585Subproblem 2
x + -7.75 = -7.352720585 Simplifying x + -7.75 = -7.352720585 Reorder the terms: -7.75 + x = -7.352720585 Solving -7.75 + x = -7.352720585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = -7.352720585 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = -7.352720585 + 7.75 x = -7.352720585 + 7.75 Combine like terms: -7.352720585 + 7.75 = 0.397279415 x = 0.397279415 Simplifying x = 0.397279415Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.102720585, 0.397279415}
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