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Simplifying 5x2 + 31x + -6 = 0 Reorder the terms: -6 + 31x + 5x2 = 0 Solving -6 + 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'. -1.2 + 6.2x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 6.2x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 6.2x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 6.2x + x2 = 0 + 1.2 6.2x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 6.2x + x2 = 1.2 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 = 1.2 + 9.61 Reorder the terms: 9.61 + 6.2x + x2 = 1.2 + 9.61 Combine like terms: 1.2 + 9.61 = 10.81 9.61 + 6.2x + x2 = 10.81 Factor a perfect square on the left side: (x + 3.1)(x + 3.1) = 10.81 Calculate the square root of the right side: 3.287856445 Break this problem into two subproblems by setting (x + 3.1) equal to 3.287856445 and -3.287856445.Subproblem 1
x + 3.1 = 3.287856445 Simplifying x + 3.1 = 3.287856445 Reorder the terms: 3.1 + x = 3.287856445 Solving 3.1 + x = 3.287856445 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 = 3.287856445 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = 3.287856445 + -3.1 x = 3.287856445 + -3.1 Combine like terms: 3.287856445 + -3.1 = 0.187856445 x = 0.187856445 Simplifying x = 0.187856445Subproblem 2
x + 3.1 = -3.287856445 Simplifying x + 3.1 = -3.287856445 Reorder the terms: 3.1 + x = -3.287856445 Solving 3.1 + x = -3.287856445 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 = -3.287856445 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = -3.287856445 + -3.1 x = -3.287856445 + -3.1 Combine like terms: -3.287856445 + -3.1 = -6.387856445 x = -6.387856445 Simplifying x = -6.387856445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.187856445, -6.387856445}
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