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Simplifying 15x2 + 40x = 168 Reorder the terms: 40x + 15x2 = 168 Solving 40x + 15x2 = 168 Solving for variable 'x'. Reorder the terms: -168 + 40x + 15x2 = 168 + -168 Combine like terms: 168 + -168 = 0 -168 + 40x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -11.2 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + 2.666666667x + 11.2 + x2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + 2.666666667x + x2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + 2.666666667x + x2 = 0 + 11.2 2.666666667x + x2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 2.666666667x + x2 = 11.2 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 11.2 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 11.2 + 1.777777780 Combine like terms: 11.2 + 1.777777780 = 12.97777778 1.777777780 + 2.666666667x + x2 = 12.97777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 12.97777778 Calculate the square root of the right side: 3.60246829 Break this problem into two subproblems by setting (x + 1.333333334) equal to 3.60246829 and -3.60246829.Subproblem 1
x + 1.333333334 = 3.60246829 Simplifying x + 1.333333334 = 3.60246829 Reorder the terms: 1.333333334 + x = 3.60246829 Solving 1.333333334 + x = 3.60246829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 3.60246829 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 3.60246829 + -1.333333334 x = 3.60246829 + -1.333333334 Combine like terms: 3.60246829 + -1.333333334 = 2.269134956 x = 2.269134956 Simplifying x = 2.269134956Subproblem 2
x + 1.333333334 = -3.60246829 Simplifying x + 1.333333334 = -3.60246829 Reorder the terms: 1.333333334 + x = -3.60246829 Solving 1.333333334 + x = -3.60246829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -3.60246829 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -3.60246829 + -1.333333334 x = -3.60246829 + -1.333333334 Combine like terms: -3.60246829 + -1.333333334 = -4.935801624 x = -4.935801624 Simplifying x = -4.935801624Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.269134956, -4.935801624}
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