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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 = 0.673611113 1.173611113 + 2.166666667x + x2 = 0.673611113 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 0.673611113 Calculate the square root of the right side: 0.820738151 Break this problem into two subproblems by setting (x + 1.083333334) equal to 0.820738151 and -0.820738151.Subproblem 1
x + 1.083333334 = 0.820738151 Simplifying x + 1.083333334 = 0.820738151 Reorder the terms: 1.083333334 + x = 0.820738151 Solving 1.083333334 + x = 0.820738151 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 = 0.820738151 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 0.820738151 + -1.083333334 x = 0.820738151 + -1.083333334 Combine like terms: 0.820738151 + -1.083333334 = -0.262595183 x = -0.262595183 Simplifying x = -0.262595183Subproblem 2
x + 1.083333334 = -0.820738151 Simplifying x + 1.083333334 = -0.820738151 Reorder the terms: 1.083333334 + x = -0.820738151 Solving 1.083333334 + x = -0.820738151 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 = -0.820738151 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -0.820738151 + -1.083333334 x = -0.820738151 + -1.083333334 Combine like terms: -0.820738151 + -1.083333334 = -1.904071485 x = -1.904071485 Simplifying x = -1.904071485Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.262595183, -1.904071485}
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