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Simplifying 28x2 + -31x + -13 = 0 Reorder the terms: -13 + -31x + 28x2 = 0 Solving -13 + -31x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.4642857143 + -1.107142857x + x2 = 0 Move the constant term to the right: Add '0.4642857143' to each side of the equation. -0.4642857143 + -1.107142857x + 0.4642857143 + x2 = 0 + 0.4642857143 Reorder the terms: -0.4642857143 + 0.4642857143 + -1.107142857x + x2 = 0 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + -1.107142857x + x2 = 0 + 0.4642857143 -1.107142857x + x2 = 0 + 0.4642857143 Combine like terms: 0 + 0.4642857143 = 0.4642857143 -1.107142857x + x2 = 0.4642857143 The x term is -1.107142857x. Take half its coefficient (-0.5535714285). Square it (0.3064413265) and add it to both sides. Add '0.3064413265' to each side of the equation. -1.107142857x + 0.3064413265 + x2 = 0.4642857143 + 0.3064413265 Reorder the terms: 0.3064413265 + -1.107142857x + x2 = 0.4642857143 + 0.3064413265 Combine like terms: 0.4642857143 + 0.3064413265 = 0.7707270408 0.3064413265 + -1.107142857x + x2 = 0.7707270408 Factor a perfect square on the left side: (x + -0.5535714285)(x + -0.5535714285) = 0.7707270408 Calculate the square root of the right side: 0.877910611 Break this problem into two subproblems by setting (x + -0.5535714285) equal to 0.877910611 and -0.877910611.Subproblem 1
x + -0.5535714285 = 0.877910611 Simplifying x + -0.5535714285 = 0.877910611 Reorder the terms: -0.5535714285 + x = 0.877910611 Solving -0.5535714285 + x = 0.877910611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5535714285' to each side of the equation. -0.5535714285 + 0.5535714285 + x = 0.877910611 + 0.5535714285 Combine like terms: -0.5535714285 + 0.5535714285 = 0.0000000000 0.0000000000 + x = 0.877910611 + 0.5535714285 x = 0.877910611 + 0.5535714285 Combine like terms: 0.877910611 + 0.5535714285 = 1.4314820395 x = 1.4314820395 Simplifying x = 1.4314820395Subproblem 2
x + -0.5535714285 = -0.877910611 Simplifying x + -0.5535714285 = -0.877910611 Reorder the terms: -0.5535714285 + x = -0.877910611 Solving -0.5535714285 + x = -0.877910611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5535714285' to each side of the equation. -0.5535714285 + 0.5535714285 + x = -0.877910611 + 0.5535714285 Combine like terms: -0.5535714285 + 0.5535714285 = 0.0000000000 0.0000000000 + x = -0.877910611 + 0.5535714285 x = -0.877910611 + 0.5535714285 Combine like terms: -0.877910611 + 0.5535714285 = -0.3243391825 x = -0.3243391825 Simplifying x = -0.3243391825Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4314820395, -0.3243391825}
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