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Simplifying 2x2 + -31x + 21 = 0 Reorder the terms: 21 + -31x + 2x2 = 0 Solving 21 + -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'. 10.5 + -15.5x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -15.5x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -15.5x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -15.5x + x2 = 0 + -10.5 -15.5x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -15.5x + x2 = -10.5 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 = -10.5 + 60.0625 Reorder the terms: 60.0625 + -15.5x + x2 = -10.5 + 60.0625 Combine like terms: -10.5 + 60.0625 = 49.5625 60.0625 + -15.5x + x2 = 49.5625 Factor a perfect square on the left side: (x + -7.75)(x + -7.75) = 49.5625 Calculate the square root of the right side: 7.04006392 Break this problem into two subproblems by setting (x + -7.75) equal to 7.04006392 and -7.04006392.Subproblem 1
x + -7.75 = 7.04006392 Simplifying x + -7.75 = 7.04006392 Reorder the terms: -7.75 + x = 7.04006392 Solving -7.75 + x = 7.04006392 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 = 7.04006392 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = 7.04006392 + 7.75 x = 7.04006392 + 7.75 Combine like terms: 7.04006392 + 7.75 = 14.79006392 x = 14.79006392 Simplifying x = 14.79006392Subproblem 2
x + -7.75 = -7.04006392 Simplifying x + -7.75 = -7.04006392 Reorder the terms: -7.75 + x = -7.04006392 Solving -7.75 + x = -7.04006392 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 = -7.04006392 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = -7.04006392 + 7.75 x = -7.04006392 + 7.75 Combine like terms: -7.04006392 + 7.75 = 0.70993608 x = 0.70993608 Simplifying x = 0.70993608Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.79006392, 0.70993608}
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