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Simplifying -3x(2x + 7) + 5x = -13 Reorder the terms: -3x(7 + 2x) + 5x = -13 (7 * -3x + 2x * -3x) + 5x = -13 (-21x + -6x2) + 5x = -13 Reorder the terms: -21x + 5x + -6x2 = -13 Combine like terms: -21x + 5x = -16x -16x + -6x2 = -13 Solving -16x + -6x2 = -13 Solving for variable 'x'. Reorder the terms: 13 + -16x + -6x2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + -16x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -2.166666667 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + 2.666666667x + 2.166666667 + x2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + 2.666666667x + x2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + 2.666666667x + x2 = 0 + 2.166666667 2.666666667x + x2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 2.666666667x + x2 = 2.166666667 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 = 2.166666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 2.166666667 + 1.777777780 Combine like terms: 2.166666667 + 1.777777780 = 3.944444447 1.777777780 + 2.666666667x + x2 = 3.944444447 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 3.944444447 Calculate the square root of the right side: 1.986062549 Break this problem into two subproblems by setting (x + 1.333333334) equal to 1.986062549 and -1.986062549.Subproblem 1
x + 1.333333334 = 1.986062549 Simplifying x + 1.333333334 = 1.986062549 Reorder the terms: 1.333333334 + x = 1.986062549 Solving 1.333333334 + x = 1.986062549 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 = 1.986062549 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.986062549 + -1.333333334 x = 1.986062549 + -1.333333334 Combine like terms: 1.986062549 + -1.333333334 = 0.652729215 x = 0.652729215 Simplifying x = 0.652729215Subproblem 2
x + 1.333333334 = -1.986062549 Simplifying x + 1.333333334 = -1.986062549 Reorder the terms: 1.333333334 + x = -1.986062549 Solving 1.333333334 + x = -1.986062549 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 = -1.986062549 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.986062549 + -1.333333334 x = -1.986062549 + -1.333333334 Combine like terms: -1.986062549 + -1.333333334 = -3.319395883 x = -3.319395883 Simplifying x = -3.319395883Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.652729215, -3.319395883}
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