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Simplifying 8x(x + 24) = 384 Reorder the terms: 8x(24 + x) = 384 (24 * 8x + x * 8x) = 384 (192x + 8x2) = 384 Solving 192x + 8x2 = 384 Solving for variable 'x'. Reorder the terms: -384 + 192x + 8x2 = 384 + -384 Combine like terms: 384 + -384 = 0 -384 + 192x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-48 + 24x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-48 + 24x + x2)' equal to zero and attempt to solve: Simplifying -48 + 24x + x2 = 0 Solving -48 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 24x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 24x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 24x + x2 = 0 + 48 24x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 24x + x2 = 48 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 48 + 144 Reorder the terms: 144 + 24x + x2 = 48 + 144 Combine like terms: 48 + 144 = 192 144 + 24x + x2 = 192 Factor a perfect square on the left side: (x + 12)(x + 12) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (x + 12) equal to 13.856406461 and -13.856406461.Subproblem 1
x + 12 = 13.856406461 Simplifying x + 12 = 13.856406461 Reorder the terms: 12 + x = 13.856406461 Solving 12 + x = 13.856406461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 13.856406461 + -12 Combine like terms: 12 + -12 = 0 0 + x = 13.856406461 + -12 x = 13.856406461 + -12 Combine like terms: 13.856406461 + -12 = 1.856406461 x = 1.856406461 Simplifying x = 1.856406461Subproblem 2
x + 12 = -13.856406461 Simplifying x + 12 = -13.856406461 Reorder the terms: 12 + x = -13.856406461 Solving 12 + x = -13.856406461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -13.856406461 + -12 Combine like terms: 12 + -12 = 0 0 + x = -13.856406461 + -12 x = -13.856406461 + -12 Combine like terms: -13.856406461 + -12 = -25.856406461 x = -25.856406461 Simplifying x = -25.856406461Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.856406461, -25.856406461}Solution
x = {1.856406461, -25.856406461}
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