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Simplifying 6x(x + 3) + x = 6x + 3 + 15 Reorder the terms: 6x(3 + x) + x = 6x + 3 + 15 (3 * 6x + x * 6x) + x = 6x + 3 + 15 (18x + 6x2) + x = 6x + 3 + 15 Reorder the terms: 18x + x + 6x2 = 6x + 3 + 15 Combine like terms: 18x + x = 19x 19x + 6x2 = 6x + 3 + 15 Reorder the terms: 19x + 6x2 = 3 + 15 + 6x Combine like terms: 3 + 15 = 18 19x + 6x2 = 18 + 6x Solving 19x + 6x2 = 18 + 6x Solving for variable 'x'. Reorder the terms: -18 + 19x + -6x + 6x2 = 18 + 6x + -18 + -6x Combine like terms: 19x + -6x = 13x -18 + 13x + 6x2 = 18 + 6x + -18 + -6x Reorder the terms: -18 + 13x + 6x2 = 18 + -18 + 6x + -6x Combine like terms: 18 + -18 = 0 -18 + 13x + 6x2 = 0 + 6x + -6x -18 + 13x + 6x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -18 + 13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.166666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.166666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.166666667x + x2 = 0 + 3 2.166666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.166666667x + x2 = 3 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 = 3 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = 3 + 1.173611113 Combine like terms: 3 + 1.173611113 = 4.173611113 1.173611113 + 2.166666667x + x2 = 4.173611113 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 4.173611113 Calculate the square root of the right side: 2.042941779 Break this problem into two subproblems by setting (x + 1.083333334) equal to 2.042941779 and -2.042941779.Subproblem 1
x + 1.083333334 = 2.042941779 Simplifying x + 1.083333334 = 2.042941779 Reorder the terms: 1.083333334 + x = 2.042941779 Solving 1.083333334 + x = 2.042941779 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 = 2.042941779 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 2.042941779 + -1.083333334 x = 2.042941779 + -1.083333334 Combine like terms: 2.042941779 + -1.083333334 = 0.959608445 x = 0.959608445 Simplifying x = 0.959608445Subproblem 2
x + 1.083333334 = -2.042941779 Simplifying x + 1.083333334 = -2.042941779 Reorder the terms: 1.083333334 + x = -2.042941779 Solving 1.083333334 + x = -2.042941779 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 = -2.042941779 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -2.042941779 + -1.083333334 x = -2.042941779 + -1.083333334 Combine like terms: -2.042941779 + -1.083333334 = -3.126275113 x = -3.126275113 Simplifying x = -3.126275113Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.959608445, -3.126275113}
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