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Simplifying -5x2 + -31x + -28 = 0 Reorder the terms: -28 + -31x + -5x2 = 0 Solving -28 + -31x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(28 + 31x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(28 + 31x + 5x2)' equal to zero and attempt to solve: Simplifying 28 + 31x + 5x2 = 0 Solving 28 + 31x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.6 + 6.2x + x2 = 0 Move the constant term to the right: Add '-5.6' to each side of the equation. 5.6 + 6.2x + -5.6 + x2 = 0 + -5.6 Reorder the terms: 5.6 + -5.6 + 6.2x + x2 = 0 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + 6.2x + x2 = 0 + -5.6 6.2x + x2 = 0 + -5.6 Combine like terms: 0 + -5.6 = -5.6 6.2x + x2 = -5.6 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 = -5.6 + 9.61 Reorder the terms: 9.61 + 6.2x + x2 = -5.6 + 9.61 Combine like terms: -5.6 + 9.61 = 4.01 9.61 + 6.2x + x2 = 4.01 Factor a perfect square on the left side: (x + 3.1)(x + 3.1) = 4.01 Calculate the square root of the right side: 2.002498439 Break this problem into two subproblems by setting (x + 3.1) equal to 2.002498439 and -2.002498439.Subproblem 1
x + 3.1 = 2.002498439 Simplifying x + 3.1 = 2.002498439 Reorder the terms: 3.1 + x = 2.002498439 Solving 3.1 + x = 2.002498439 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 = 2.002498439 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = 2.002498439 + -3.1 x = 2.002498439 + -3.1 Combine like terms: 2.002498439 + -3.1 = -1.097501561 x = -1.097501561 Simplifying x = -1.097501561Subproblem 2
x + 3.1 = -2.002498439 Simplifying x + 3.1 = -2.002498439 Reorder the terms: 3.1 + x = -2.002498439 Solving 3.1 + x = -2.002498439 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 = -2.002498439 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = -2.002498439 + -3.1 x = -2.002498439 + -3.1 Combine like terms: -2.002498439 + -3.1 = -5.102498439 x = -5.102498439 Simplifying x = -5.102498439Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.097501561, -5.102498439}Solution
x = {-1.097501561, -5.102498439}
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