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Simplifying 3x2 + 13x + -31 = 0 Reorder the terms: -31 + 13x + 3x2 = 0 Solving -31 + 13x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.33333333 + 4.333333333x + x2 = 0 Move the constant term to the right: Add '10.33333333' to each side of the equation. -10.33333333 + 4.333333333x + 10.33333333 + x2 = 0 + 10.33333333 Reorder the terms: -10.33333333 + 10.33333333 + 4.333333333x + x2 = 0 + 10.33333333 Combine like terms: -10.33333333 + 10.33333333 = 0.00000000 0.00000000 + 4.333333333x + x2 = 0 + 10.33333333 4.333333333x + x2 = 0 + 10.33333333 Combine like terms: 0 + 10.33333333 = 10.33333333 4.333333333x + x2 = 10.33333333 The x term is 4.333333333x. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333x + 4.694444446 + x2 = 10.33333333 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333x + x2 = 10.33333333 + 4.694444446 Combine like terms: 10.33333333 + 4.694444446 = 15.027777776 4.694444446 + 4.333333333x + x2 = 15.027777776 Factor a perfect square on the left side: (x + 2.166666667)(x + 2.166666667) = 15.027777776 Calculate the square root of the right side: 3.876567783 Break this problem into two subproblems by setting (x + 2.166666667) equal to 3.876567783 and -3.876567783.Subproblem 1
x + 2.166666667 = 3.876567783 Simplifying x + 2.166666667 = 3.876567783 Reorder the terms: 2.166666667 + x = 3.876567783 Solving 2.166666667 + x = 3.876567783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 3.876567783 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 3.876567783 + -2.166666667 x = 3.876567783 + -2.166666667 Combine like terms: 3.876567783 + -2.166666667 = 1.709901116 x = 1.709901116 Simplifying x = 1.709901116Subproblem 2
x + 2.166666667 = -3.876567783 Simplifying x + 2.166666667 = -3.876567783 Reorder the terms: 2.166666667 + x = -3.876567783 Solving 2.166666667 + x = -3.876567783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -3.876567783 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -3.876567783 + -2.166666667 x = -3.876567783 + -2.166666667 Combine like terms: -3.876567783 + -2.166666667 = -6.04323445 x = -6.04323445 Simplifying x = -6.04323445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.709901116, -6.04323445}
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