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Simplifying 9x(x + 3) = 2(x + 4) + 7 Reorder the terms: 9x(3 + x) = 2(x + 4) + 7 (3 * 9x + x * 9x) = 2(x + 4) + 7 (27x + 9x2) = 2(x + 4) + 7 Reorder the terms: 27x + 9x2 = 2(4 + x) + 7 27x + 9x2 = (4 * 2 + x * 2) + 7 27x + 9x2 = (8 + 2x) + 7 Reorder the terms: 27x + 9x2 = 8 + 7 + 2x Combine like terms: 8 + 7 = 15 27x + 9x2 = 15 + 2x Solving 27x + 9x2 = 15 + 2x Solving for variable 'x'. Reorder the terms: -15 + 27x + -2x + 9x2 = 15 + 2x + -15 + -2x Combine like terms: 27x + -2x = 25x -15 + 25x + 9x2 = 15 + 2x + -15 + -2x Reorder the terms: -15 + 25x + 9x2 = 15 + -15 + 2x + -2x Combine like terms: 15 + -15 = 0 -15 + 25x + 9x2 = 0 + 2x + -2x -15 + 25x + 9x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -15 + 25x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.666666667 + 2.777777778x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 2.777777778x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 2.777777778x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 2.777777778x + x2 = 0 + 1.666666667 2.777777778x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 2.777777778x + x2 = 1.666666667 The x term is 2.777777778x. Take half its coefficient (1.388888889). Square it (1.929012346) and add it to both sides. Add '1.929012346' to each side of the equation. 2.777777778x + 1.929012346 + x2 = 1.666666667 + 1.929012346 Reorder the terms: 1.929012346 + 2.777777778x + x2 = 1.666666667 + 1.929012346 Combine like terms: 1.666666667 + 1.929012346 = 3.595679013 1.929012346 + 2.777777778x + x2 = 3.595679013 Factor a perfect square on the left side: (x + 1.388888889)(x + 1.388888889) = 3.595679013 Calculate the square root of the right side: 1.896227574 Break this problem into two subproblems by setting (x + 1.388888889) equal to 1.896227574 and -1.896227574.Subproblem 1
x + 1.388888889 = 1.896227574 Simplifying x + 1.388888889 = 1.896227574 Reorder the terms: 1.388888889 + x = 1.896227574 Solving 1.388888889 + x = 1.896227574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.388888889' to each side of the equation. 1.388888889 + -1.388888889 + x = 1.896227574 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = 1.896227574 + -1.388888889 x = 1.896227574 + -1.388888889 Combine like terms: 1.896227574 + -1.388888889 = 0.507338685 x = 0.507338685 Simplifying x = 0.507338685Subproblem 2
x + 1.388888889 = -1.896227574 Simplifying x + 1.388888889 = -1.896227574 Reorder the terms: 1.388888889 + x = -1.896227574 Solving 1.388888889 + x = -1.896227574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.388888889' to each side of the equation. 1.388888889 + -1.388888889 + x = -1.896227574 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = -1.896227574 + -1.388888889 x = -1.896227574 + -1.388888889 Combine like terms: -1.896227574 + -1.388888889 = -3.285116463 x = -3.285116463 Simplifying x = -3.285116463Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.507338685, -3.285116463}
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