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Simplifying 5(x + 9)(x + 9) = 60 Reorder the terms: 5(9 + x)(x + 9) = 60 Reorder the terms: 5(9 + x)(9 + x) = 60 Multiply (9 + x) * (9 + x) 5(9(9 + x) + x(9 + x)) = 60 5((9 * 9 + x * 9) + x(9 + x)) = 60 5((81 + 9x) + x(9 + x)) = 60 5(81 + 9x + (9 * x + x * x)) = 60 5(81 + 9x + (9x + x2)) = 60 Combine like terms: 9x + 9x = 18x 5(81 + 18x + x2) = 60 (81 * 5 + 18x * 5 + x2 * 5) = 60 (405 + 90x + 5x2) = 60 Solving 405 + 90x + 5x2 = 60 Solving for variable 'x'. Reorder the terms: 405 + -60 + 90x + 5x2 = 60 + -60 Combine like terms: 405 + -60 = 345 345 + 90x + 5x2 = 60 + -60 Combine like terms: 60 + -60 = 0 345 + 90x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(69 + 18x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(69 + 18x + x2)' equal to zero and attempt to solve: Simplifying 69 + 18x + x2 = 0 Solving 69 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-69' to each side of the equation. 69 + 18x + -69 + x2 = 0 + -69 Reorder the terms: 69 + -69 + 18x + x2 = 0 + -69 Combine like terms: 69 + -69 = 0 0 + 18x + x2 = 0 + -69 18x + x2 = 0 + -69 Combine like terms: 0 + -69 = -69 18x + x2 = -69 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -69 + 81 Reorder the terms: 81 + 18x + x2 = -69 + 81 Combine like terms: -69 + 81 = 12 81 + 18x + x2 = 12 Factor a perfect square on the left side: (x + 9)(x + 9) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 9) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 9 = 3.464101615 Simplifying x + 9 = 3.464101615 Reorder the terms: 9 + x = 3.464101615 Solving 9 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 3.464101615 + -9 Combine like terms: 9 + -9 = 0 0 + x = 3.464101615 + -9 x = 3.464101615 + -9 Combine like terms: 3.464101615 + -9 = -5.535898385 x = -5.535898385 Simplifying x = -5.535898385Subproblem 2
x + 9 = -3.464101615 Simplifying x + 9 = -3.464101615 Reorder the terms: 9 + x = -3.464101615 Solving 9 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -3.464101615 + -9 Combine like terms: 9 + -9 = 0 0 + x = -3.464101615 + -9 x = -3.464101615 + -9 Combine like terms: -3.464101615 + -9 = -12.464101615 x = -12.464101615 Simplifying x = -12.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.535898385, -12.464101615}Solution
x = {-5.535898385, -12.464101615}
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