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Simplifying 31x2 + 8x + -3 = 0 Reorder the terms: -3 + 8x + 31x2 = 0 Solving -3 + 8x + 31x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 31 the coefficient of the squared term: Divide each side by '31'. -0.09677419355 + 0.2580645161x + x2 = 0 Move the constant term to the right: Add '0.09677419355' to each side of the equation. -0.09677419355 + 0.2580645161x + 0.09677419355 + x2 = 0 + 0.09677419355 Reorder the terms: -0.09677419355 + 0.09677419355 + 0.2580645161x + x2 = 0 + 0.09677419355 Combine like terms: -0.09677419355 + 0.09677419355 = 0.00000000000 0.00000000000 + 0.2580645161x + x2 = 0 + 0.09677419355 0.2580645161x + x2 = 0 + 0.09677419355 Combine like terms: 0 + 0.09677419355 = 0.09677419355 0.2580645161x + x2 = 0.09677419355 The x term is 0.2580645161x. Take half its coefficient (0.1290322581). Square it (0.01664932363) and add it to both sides. Add '0.01664932363' to each side of the equation. 0.2580645161x + 0.01664932363 + x2 = 0.09677419355 + 0.01664932363 Reorder the terms: 0.01664932363 + 0.2580645161x + x2 = 0.09677419355 + 0.01664932363 Combine like terms: 0.09677419355 + 0.01664932363 = 0.11342351718 0.01664932363 + 0.2580645161x + x2 = 0.11342351718 Factor a perfect square on the left side: (x + 0.1290322581)(x + 0.1290322581) = 0.11342351718 Calculate the square root of the right side: 0.336784081 Break this problem into two subproblems by setting (x + 0.1290322581) equal to 0.336784081 and -0.336784081.Subproblem 1
x + 0.1290322581 = 0.336784081 Simplifying x + 0.1290322581 = 0.336784081 Reorder the terms: 0.1290322581 + x = 0.336784081 Solving 0.1290322581 + x = 0.336784081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1290322581' to each side of the equation. 0.1290322581 + -0.1290322581 + x = 0.336784081 + -0.1290322581 Combine like terms: 0.1290322581 + -0.1290322581 = 0.0000000000 0.0000000000 + x = 0.336784081 + -0.1290322581 x = 0.336784081 + -0.1290322581 Combine like terms: 0.336784081 + -0.1290322581 = 0.2077518229 x = 0.2077518229 Simplifying x = 0.2077518229Subproblem 2
x + 0.1290322581 = -0.336784081 Simplifying x + 0.1290322581 = -0.336784081 Reorder the terms: 0.1290322581 + x = -0.336784081 Solving 0.1290322581 + x = -0.336784081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1290322581' to each side of the equation. 0.1290322581 + -0.1290322581 + x = -0.336784081 + -0.1290322581 Combine like terms: 0.1290322581 + -0.1290322581 = 0.0000000000 0.0000000000 + x = -0.336784081 + -0.1290322581 x = -0.336784081 + -0.1290322581 Combine like terms: -0.336784081 + -0.1290322581 = -0.4658163391 x = -0.4658163391 Simplifying x = -0.4658163391Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2077518229, -0.4658163391}
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