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Simplifying 3x(x + -3) + 13 = 2(x + 5) Reorder the terms: 3x(-3 + x) + 13 = 2(x + 5) (-3 * 3x + x * 3x) + 13 = 2(x + 5) (-9x + 3x2) + 13 = 2(x + 5) Reorder the terms: 13 + -9x + 3x2 = 2(x + 5) Reorder the terms: 13 + -9x + 3x2 = 2(5 + x) 13 + -9x + 3x2 = (5 * 2 + x * 2) 13 + -9x + 3x2 = (10 + 2x) Solving 13 + -9x + 3x2 = 10 + 2x Solving for variable 'x'. Reorder the terms: 13 + -10 + -9x + -2x + 3x2 = 10 + 2x + -10 + -2x Combine like terms: 13 + -10 = 3 3 + -9x + -2x + 3x2 = 10 + 2x + -10 + -2x Combine like terms: -9x + -2x = -11x 3 + -11x + 3x2 = 10 + 2x + -10 + -2x Reorder the terms: 3 + -11x + 3x2 = 10 + -10 + 2x + -2x Combine like terms: 10 + -10 = 0 3 + -11x + 3x2 = 0 + 2x + -2x 3 + -11x + 3x2 = 2x + -2x Combine like terms: 2x + -2x = 0 3 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.666666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -3.666666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.666666667x + x2 = 0 + -1 -3.666666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.666666667x + x2 = -1 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = -1 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = -1 + 3.361111114 Combine like terms: -1 + 3.361111114 = 2.361111114 3.361111114 + -3.666666667x + x2 = 2.361111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 2.361111114 Calculate the square root of the right side: 1.536590744 Break this problem into two subproblems by setting (x + -1.833333334) equal to 1.536590744 and -1.536590744.Subproblem 1
x + -1.833333334 = 1.536590744 Simplifying x + -1.833333334 = 1.536590744 Reorder the terms: -1.833333334 + x = 1.536590744 Solving -1.833333334 + x = 1.536590744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 1.536590744 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 1.536590744 + 1.833333334 x = 1.536590744 + 1.833333334 Combine like terms: 1.536590744 + 1.833333334 = 3.369924078 x = 3.369924078 Simplifying x = 3.369924078Subproblem 2
x + -1.833333334 = -1.536590744 Simplifying x + -1.833333334 = -1.536590744 Reorder the terms: -1.833333334 + x = -1.536590744 Solving -1.833333334 + x = -1.536590744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -1.536590744 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -1.536590744 + 1.833333334 x = -1.536590744 + 1.833333334 Combine like terms: -1.536590744 + 1.833333334 = 0.29674259 x = 0.29674259 Simplifying x = 0.29674259Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.369924078, 0.29674259}
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