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Simplifying 6x2 + 13x = 3 Reorder the terms: 13x + 6x2 = 3 Solving 13x + 6x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 13x + 6x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2.166666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2.166666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2.166666667x + x2 = 0 + 0.5 2.166666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2.166666667x + x2 = 0.5 The x term is 2.166666667x. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667x + 1.173611113 + x2 = 0.5 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = 0.5 + 1.173611113 Combine like terms: 0.5 + 1.173611113 = 1.673611113 1.173611113 + 2.166666667x + x2 = 1.673611113 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 1.673611113 Calculate the square root of the right side: 1.293681225 Break this problem into two subproblems by setting (x + 1.083333334) equal to 1.293681225 and -1.293681225.Subproblem 1
x + 1.083333334 = 1.293681225 Simplifying x + 1.083333334 = 1.293681225 Reorder the terms: 1.083333334 + x = 1.293681225 Solving 1.083333334 + x = 1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = 1.293681225 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 1.293681225 + -1.083333334 x = 1.293681225 + -1.083333334 Combine like terms: 1.293681225 + -1.083333334 = 0.210347891 x = 0.210347891 Simplifying x = 0.210347891Subproblem 2
x + 1.083333334 = -1.293681225 Simplifying x + 1.083333334 = -1.293681225 Reorder the terms: 1.083333334 + x = -1.293681225 Solving 1.083333334 + x = -1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = -1.293681225 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -1.293681225 + -1.083333334 x = -1.293681225 + -1.083333334 Combine like terms: -1.293681225 + -1.083333334 = -2.377014559 x = -2.377014559 Simplifying x = -2.377014559Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.210347891, -2.377014559}
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