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Simplifying (x + 9)(x + 9) = 24 Reorder the terms: (9 + x)(x + 9) = 24 Reorder the terms: (9 + x)(9 + x) = 24 Multiply (9 + x) * (9 + x) (9(9 + x) + x(9 + x)) = 24 ((9 * 9 + x * 9) + x(9 + x)) = 24 ((81 + 9x) + x(9 + x)) = 24 (81 + 9x + (9 * x + x * x)) = 24 (81 + 9x + (9x + x2)) = 24 Combine like terms: 9x + 9x = 18x (81 + 18x + x2) = 24 Solving 81 + 18x + x2 = 24 Solving for variable 'x'. Reorder the terms: 81 + -24 + 18x + x2 = 24 + -24 Combine like terms: 81 + -24 = 57 57 + 18x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 57 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-57' to each side of the equation. 57 + 18x + -57 + x2 = 0 + -57 Reorder the terms: 57 + -57 + 18x + x2 = 0 + -57 Combine like terms: 57 + -57 = 0 0 + 18x + x2 = 0 + -57 18x + x2 = 0 + -57 Combine like terms: 0 + -57 = -57 18x + x2 = -57 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 = -57 + 81 Reorder the terms: 81 + 18x + x2 = -57 + 81 Combine like terms: -57 + 81 = 24 81 + 18x + x2 = 24 Factor a perfect square on the left side: (x + 9)(x + 9) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 9) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 9 = 4.898979486 Simplifying x + 9 = 4.898979486 Reorder the terms: 9 + x = 4.898979486 Solving 9 + x = 4.898979486 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 = 4.898979486 + -9 Combine like terms: 9 + -9 = 0 0 + x = 4.898979486 + -9 x = 4.898979486 + -9 Combine like terms: 4.898979486 + -9 = -4.101020514 x = -4.101020514 Simplifying x = -4.101020514Subproblem 2
x + 9 = -4.898979486 Simplifying x + 9 = -4.898979486 Reorder the terms: 9 + x = -4.898979486 Solving 9 + x = -4.898979486 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 = -4.898979486 + -9 Combine like terms: 9 + -9 = 0 0 + x = -4.898979486 + -9 x = -4.898979486 + -9 Combine like terms: -4.898979486 + -9 = -13.898979486 x = -13.898979486 Simplifying x = -13.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.101020514, -13.898979486}
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