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Simplifying 5x2 + 31x + 2 = 0 Reorder the terms: 2 + 31x + 5x2 = 0 Solving 2 + 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'. 0.4 + 6.2x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 6.2x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 6.2x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 6.2x + x2 = 0 + -0.4 6.2x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 6.2x + x2 = -0.4 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 = -0.4 + 9.61 Reorder the terms: 9.61 + 6.2x + x2 = -0.4 + 9.61 Combine like terms: -0.4 + 9.61 = 9.21 9.61 + 6.2x + x2 = 9.21 Factor a perfect square on the left side: (x + 3.1)(x + 3.1) = 9.21 Calculate the square root of the right side: 3.034798181 Break this problem into two subproblems by setting (x + 3.1) equal to 3.034798181 and -3.034798181.Subproblem 1
x + 3.1 = 3.034798181 Simplifying x + 3.1 = 3.034798181 Reorder the terms: 3.1 + x = 3.034798181 Solving 3.1 + x = 3.034798181 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 = 3.034798181 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = 3.034798181 + -3.1 x = 3.034798181 + -3.1 Combine like terms: 3.034798181 + -3.1 = -0.065201819 x = -0.065201819 Simplifying x = -0.065201819Subproblem 2
x + 3.1 = -3.034798181 Simplifying x + 3.1 = -3.034798181 Reorder the terms: 3.1 + x = -3.034798181 Solving 3.1 + x = -3.034798181 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 = -3.034798181 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = -3.034798181 + -3.1 x = -3.034798181 + -3.1 Combine like terms: -3.034798181 + -3.1 = -6.134798181 x = -6.134798181 Simplifying x = -6.134798181Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.065201819, -6.134798181}
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