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Simplifying -5x + 3x(x + -7) = -39 Reorder the terms: -5x + 3x(-7 + x) = -39 -5x + (-7 * 3x + x * 3x) = -39 -5x + (-21x + 3x2) = -39 Combine like terms: -5x + -21x = -26x -26x + 3x2 = -39 Solving -26x + 3x2 = -39 Solving for variable 'x'. Reorder the terms: 39 + -26x + 3x2 = -39 + 39 Combine like terms: -39 + 39 = 0 39 + -26x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 13 + -8.666666667x + x2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + -8.666666667x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -8.666666667x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8.666666667x + x2 = 0 + -13 -8.666666667x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -8.666666667x + x2 = -13 The x term is -8.666666667x. Take half its coefficient (-4.333333334). Square it (18.77777778) and add it to both sides. Add '18.77777778' to each side of the equation. -8.666666667x + 18.77777778 + x2 = -13 + 18.77777778 Reorder the terms: 18.77777778 + -8.666666667x + x2 = -13 + 18.77777778 Combine like terms: -13 + 18.77777778 = 5.77777778 18.77777778 + -8.666666667x + x2 = 5.77777778 Factor a perfect square on the left side: (x + -4.333333334)(x + -4.333333334) = 5.77777778 Calculate the square root of the right side: 2.403700851 Break this problem into two subproblems by setting (x + -4.333333334) equal to 2.403700851 and -2.403700851.Subproblem 1
x + -4.333333334 = 2.403700851 Simplifying x + -4.333333334 = 2.403700851 Reorder the terms: -4.333333334 + x = 2.403700851 Solving -4.333333334 + x = 2.403700851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = 2.403700851 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = 2.403700851 + 4.333333334 x = 2.403700851 + 4.333333334 Combine like terms: 2.403700851 + 4.333333334 = 6.737034185 x = 6.737034185 Simplifying x = 6.737034185Subproblem 2
x + -4.333333334 = -2.403700851 Simplifying x + -4.333333334 = -2.403700851 Reorder the terms: -4.333333334 + x = -2.403700851 Solving -4.333333334 + x = -2.403700851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = -2.403700851 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = -2.403700851 + 4.333333334 x = -2.403700851 + 4.333333334 Combine like terms: -2.403700851 + 4.333333334 = 1.929632483 x = 1.929632483 Simplifying x = 1.929632483Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.737034185, 1.929632483}
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