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Simplifying 144 = (12 + x)(8 + x) Multiply (12 + x) * (8 + x) 144 = (12(8 + x) + x(8 + x)) 144 = ((8 * 12 + x * 12) + x(8 + x)) 144 = ((96 + 12x) + x(8 + x)) 144 = (96 + 12x + (8 * x + x * x)) 144 = (96 + 12x + (8x + x2)) Combine like terms: 12x + 8x = 20x 144 = (96 + 20x + x2) Solving 144 = 96 + 20x + x2 Solving for variable 'x'. Combine like terms: 144 + -96 = 48 48 + -20x + -1x2 = 96 + 20x + x2 + -96 + -20x + -1x2 Reorder the terms: 48 + -20x + -1x2 = 96 + -96 + 20x + -20x + x2 + -1x2 Combine like terms: 96 + -96 = 0 48 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2 48 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 48 + -20x + -1x2 = 0 + x2 + -1x2 48 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 48 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 20x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 20x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 20x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 20x + x2 = 0 + 48 20x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 20x + x2 = 48 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 48 + 100 Reorder the terms: 100 + 20x + x2 = 48 + 100 Combine like terms: 48 + 100 = 148 100 + 20x + x2 = 148 Factor a perfect square on the left side: (x + 10)(x + 10) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (x + 10) equal to 12.165525061 and -12.165525061.Subproblem 1
x + 10 = 12.165525061 Simplifying x + 10 = 12.165525061 Reorder the terms: 10 + x = 12.165525061 Solving 10 + x = 12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 12.165525061 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.165525061 + -10 x = 12.165525061 + -10 Combine like terms: 12.165525061 + -10 = 2.165525061 x = 2.165525061 Simplifying x = 2.165525061Subproblem 2
x + 10 = -12.165525061 Simplifying x + 10 = -12.165525061 Reorder the terms: 10 + x = -12.165525061 Solving 10 + x = -12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -12.165525061 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.165525061 + -10 x = -12.165525061 + -10 Combine like terms: -12.165525061 + -10 = -22.165525061 x = -22.165525061 Simplifying x = -22.165525061Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.165525061, -22.165525061}
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