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Simplifying (x + 8)(x + 8) = 24 Reorder the terms: (8 + x)(x + 8) = 24 Reorder the terms: (8 + x)(8 + x) = 24 Multiply (8 + x) * (8 + x) (8(8 + x) + x(8 + x)) = 24 ((8 * 8 + x * 8) + x(8 + x)) = 24 ((64 + 8x) + x(8 + x)) = 24 (64 + 8x + (8 * x + x * x)) = 24 (64 + 8x + (8x + x2)) = 24 Combine like terms: 8x + 8x = 16x (64 + 16x + x2) = 24 Solving 64 + 16x + x2 = 24 Solving for variable 'x'. Reorder the terms: 64 + -24 + 16x + x2 = 24 + -24 Combine like terms: 64 + -24 = 40 40 + 16x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 40 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 16x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + 16x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 16x + x2 = 0 + -40 16x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 16x + x2 = -40 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -40 + 64 Reorder the terms: 64 + 16x + x2 = -40 + 64 Combine like terms: -40 + 64 = 24 64 + 16x + x2 = 24 Factor a perfect square on the left side: (x + 8)(x + 8) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 8) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 8 = 4.898979486 Simplifying x + 8 = 4.898979486 Reorder the terms: 8 + x = 4.898979486 Solving 8 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 4.898979486 + -8 Combine like terms: 8 + -8 = 0 0 + x = 4.898979486 + -8 x = 4.898979486 + -8 Combine like terms: 4.898979486 + -8 = -3.101020514 x = -3.101020514 Simplifying x = -3.101020514Subproblem 2
x + 8 = -4.898979486 Simplifying x + 8 = -4.898979486 Reorder the terms: 8 + x = -4.898979486 Solving 8 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -4.898979486 + -8 Combine like terms: 8 + -8 = 0 0 + x = -4.898979486 + -8 x = -4.898979486 + -8 Combine like terms: -4.898979486 + -8 = -12.898979486 x = -12.898979486 Simplifying x = -12.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.101020514, -12.898979486}
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