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Simplifying 192 = (2x + 2)(x + -4) Reorder the terms: 192 = (2 + 2x)(x + -4) Reorder the terms: 192 = (2 + 2x)(-4 + x) Multiply (2 + 2x) * (-4 + x) 192 = (2(-4 + x) + 2x * (-4 + x)) 192 = ((-4 * 2 + x * 2) + 2x * (-4 + x)) 192 = ((-8 + 2x) + 2x * (-4 + x)) 192 = (-8 + 2x + (-4 * 2x + x * 2x)) 192 = (-8 + 2x + (-8x + 2x2)) Combine like terms: 2x + -8x = -6x 192 = (-8 + -6x + 2x2) Solving 192 = -8 + -6x + 2x2 Solving for variable 'x'. Combine like terms: 192 + 8 = 200 200 + 6x + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2 Reorder the terms: 200 + 6x + -2x2 = -8 + 8 + -6x + 6x + 2x2 + -2x2 Combine like terms: -8 + 8 = 0 200 + 6x + -2x2 = 0 + -6x + 6x + 2x2 + -2x2 200 + 6x + -2x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 200 + 6x + -2x2 = 0 + 2x2 + -2x2 200 + 6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 200 + 6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(100 + 3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(100 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying 100 + 3x + -1x2 = 0 Solving 100 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + -3x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -3x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -3x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -3x + x2 = 0 + 100 -3x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -3x + x2 = 100 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 100 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 100 + 2.25 Combine like terms: 100 + 2.25 = 102.25 2.25 + -3x + x2 = 102.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (x + -1.5) equal to 10.111874208 and -10.111874208.Subproblem 1
x + -1.5 = 10.111874208 Simplifying x + -1.5 = 10.111874208 Reorder the terms: -1.5 + x = 10.111874208 Solving -1.5 + x = 10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 10.111874208 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 10.111874208 + 1.5 x = 10.111874208 + 1.5 Combine like terms: 10.111874208 + 1.5 = 11.611874208 x = 11.611874208 Simplifying x = 11.611874208Subproblem 2
x + -1.5 = -10.111874208 Simplifying x + -1.5 = -10.111874208 Reorder the terms: -1.5 + x = -10.111874208 Solving -1.5 + x = -10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -10.111874208 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -10.111874208 + 1.5 x = -10.111874208 + 1.5 Combine like terms: -10.111874208 + 1.5 = -8.611874208 x = -8.611874208 Simplifying x = -8.611874208Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.611874208, -8.611874208}Solution
x = {11.611874208, -8.611874208}
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