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Simplifying 5x2 + -31x + -38 = 0 Reorder the terms: -38 + -31x + 5x2 = 0 Solving -38 + -31x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.6 + -6.2x + x2 = 0 Move the constant term to the right: Add '7.6' to each side of the equation. -7.6 + -6.2x + 7.6 + x2 = 0 + 7.6 Reorder the terms: -7.6 + 7.6 + -6.2x + x2 = 0 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + -6.2x + x2 = 0 + 7.6 -6.2x + x2 = 0 + 7.6 Combine like terms: 0 + 7.6 = 7.6 -6.2x + x2 = 7.6 The x term is -6.2x. Take half its coefficient (-3.1). Square it (9.61) and add it to both sides. Add '9.61' to each side of the equation. -6.2x + 9.61 + x2 = 7.6 + 9.61 Reorder the terms: 9.61 + -6.2x + x2 = 7.6 + 9.61 Combine like terms: 7.6 + 9.61 = 17.21 9.61 + -6.2x + x2 = 17.21 Factor a perfect square on the left side: (x + -3.1)(x + -3.1) = 17.21 Calculate the square root of the right side: 4.148493703 Break this problem into two subproblems by setting (x + -3.1) equal to 4.148493703 and -4.148493703.Subproblem 1
x + -3.1 = 4.148493703 Simplifying x + -3.1 = 4.148493703 Reorder the terms: -3.1 + x = 4.148493703 Solving -3.1 + x = 4.148493703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.1' to each side of the equation. -3.1 + 3.1 + x = 4.148493703 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + x = 4.148493703 + 3.1 x = 4.148493703 + 3.1 Combine like terms: 4.148493703 + 3.1 = 7.248493703 x = 7.248493703 Simplifying x = 7.248493703Subproblem 2
x + -3.1 = -4.148493703 Simplifying x + -3.1 = -4.148493703 Reorder the terms: -3.1 + x = -4.148493703 Solving -3.1 + x = -4.148493703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.1' to each side of the equation. -3.1 + 3.1 + x = -4.148493703 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + x = -4.148493703 + 3.1 x = -4.148493703 + 3.1 Combine like terms: -4.148493703 + 3.1 = -1.048493703 x = -1.048493703 Simplifying x = -1.048493703Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.248493703, -1.048493703}
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