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Simplifying 9x(x + 5) = 3x + 49 Reorder the terms: 9x(5 + x) = 3x + 49 (5 * 9x + x * 9x) = 3x + 49 (45x + 9x2) = 3x + 49 Reorder the terms: 45x + 9x2 = 49 + 3x Solving 45x + 9x2 = 49 + 3x Solving for variable 'x'. Reorder the terms: -49 + 45x + -3x + 9x2 = 49 + 3x + -49 + -3x Combine like terms: 45x + -3x = 42x -49 + 42x + 9x2 = 49 + 3x + -49 + -3x Reorder the terms: -49 + 42x + 9x2 = 49 + -49 + 3x + -3x Combine like terms: 49 + -49 = 0 -49 + 42x + 9x2 = 0 + 3x + -3x -49 + 42x + 9x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -49 + 42x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.444444444 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '5.444444444' to each side of the equation. -5.444444444 + 4.666666667x + 5.444444444 + x2 = 0 + 5.444444444 Reorder the terms: -5.444444444 + 5.444444444 + 4.666666667x + x2 = 0 + 5.444444444 Combine like terms: -5.444444444 + 5.444444444 = 0.000000000 0.000000000 + 4.666666667x + x2 = 0 + 5.444444444 4.666666667x + x2 = 0 + 5.444444444 Combine like terms: 0 + 5.444444444 = 5.444444444 4.666666667x + x2 = 5.444444444 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = 5.444444444 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 5.444444444 + 5.444444448 Combine like terms: 5.444444444 + 5.444444448 = 10.888888892 5.444444448 + 4.666666667x + x2 = 10.888888892 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 10.888888892 Calculate the square root of the right side: 3.299831646 Break this problem into two subproblems by setting (x + 2.333333334) equal to 3.299831646 and -3.299831646.Subproblem 1
x + 2.333333334 = 3.299831646 Simplifying x + 2.333333334 = 3.299831646 Reorder the terms: 2.333333334 + x = 3.299831646 Solving 2.333333334 + x = 3.299831646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 3.299831646 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 3.299831646 + -2.333333334 x = 3.299831646 + -2.333333334 Combine like terms: 3.299831646 + -2.333333334 = 0.966498312 x = 0.966498312 Simplifying x = 0.966498312Subproblem 2
x + 2.333333334 = -3.299831646 Simplifying x + 2.333333334 = -3.299831646 Reorder the terms: 2.333333334 + x = -3.299831646 Solving 2.333333334 + x = -3.299831646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -3.299831646 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -3.299831646 + -2.333333334 x = -3.299831646 + -2.333333334 Combine like terms: -3.299831646 + -2.333333334 = -5.63316498 x = -5.63316498 Simplifying x = -5.63316498Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.966498312, -5.63316498}
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