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Simplifying [(16 + 2x)(8 + 2x)] + -1(8 * 16) = 1008 Multiply (16 + 2x) * (8 + 2x) [(16(8 + 2x) + 2x * (8 + 2x))] + -1(8 * 16) = 1008 [((8 * 16 + 2x * 16) + 2x * (8 + 2x))] + -1(8 * 16) = 1008 [((128 + 32x) + 2x * (8 + 2x))] + -1(8 * 16) = 1008 [(128 + 32x + (8 * 2x + 2x * 2x))] + -1(8 * 16) = 1008 [(128 + 32x + (16x + 4x2))] + -1(8 * 16) = 1008 Combine like terms: 32x + 16x = 48x [(128 + 48x + 4x2)] + -1(8 * 16) = 1008 [128 + 48x + 4x2] + -1(8 * 16) = 1008 Remove brackets around [128 + 48x + 4x2] 128 + 48x + 4x2 + -1(8 * 16) = 1008 Multiply 8 * 16 128 + 48x + 4x2 + -1(128) = 1008 Multiply -1 * 128 128 + 48x + 4x2 + -128 = 1008 Reorder the terms: 128 + -128 + 48x + 4x2 = 1008 Combine like terms: 128 + -128 = 0 0 + 48x + 4x2 = 1008 48x + 4x2 = 1008 Solving 48x + 4x2 = 1008 Solving for variable 'x'. Reorder the terms: -1008 + 48x + 4x2 = 1008 + -1008 Combine like terms: 1008 + -1008 = 0 -1008 + 48x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-252 + 12x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-252 + 12x + x2)' equal to zero and attempt to solve: Simplifying -252 + 12x + x2 = 0 Solving -252 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '252' to each side of the equation. -252 + 12x + 252 + x2 = 0 + 252 Reorder the terms: -252 + 252 + 12x + x2 = 0 + 252 Combine like terms: -252 + 252 = 0 0 + 12x + x2 = 0 + 252 12x + x2 = 0 + 252 Combine like terms: 0 + 252 = 252 12x + x2 = 252 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 252 + 36 Reorder the terms: 36 + 12x + x2 = 252 + 36 Combine like terms: 252 + 36 = 288 36 + 12x + x2 = 288 Factor a perfect square on the left side: (x + 6)(x + 6) = 288 Calculate the square root of the right side: 16.970562748 Break this problem into two subproblems by setting (x + 6) equal to 16.970562748 and -16.970562748.Subproblem 1
x + 6 = 16.970562748 Simplifying x + 6 = 16.970562748 Reorder the terms: 6 + x = 16.970562748 Solving 6 + x = 16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 16.970562748 + -6 Combine like terms: 6 + -6 = 0 0 + x = 16.970562748 + -6 x = 16.970562748 + -6 Combine like terms: 16.970562748 + -6 = 10.970562748 x = 10.970562748 Simplifying x = 10.970562748Subproblem 2
x + 6 = -16.970562748 Simplifying x + 6 = -16.970562748 Reorder the terms: 6 + x = -16.970562748 Solving 6 + x = -16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -16.970562748 + -6 Combine like terms: 6 + -6 = 0 0 + x = -16.970562748 + -6 x = -16.970562748 + -6 Combine like terms: -16.970562748 + -6 = -22.970562748 x = -22.970562748 Simplifying x = -22.970562748Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.970562748, -22.970562748}Solution
x = {10.970562748, -22.970562748}
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