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Simplifying (6 + x)(10 + x) = 144 Multiply (6 + x) * (10 + x) (6(10 + x) + x(10 + x)) = 144 ((10 * 6 + x * 6) + x(10 + x)) = 144 ((60 + 6x) + x(10 + x)) = 144 (60 + 6x + (10 * x + x * x)) = 144 (60 + 6x + (10x + x2)) = 144 Combine like terms: 6x + 10x = 16x (60 + 16x + x2) = 144 Solving 60 + 16x + x2 = 144 Solving for variable 'x'. Reorder the terms: 60 + -144 + 16x + x2 = 144 + -144 Combine like terms: 60 + -144 = -84 -84 + 16x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -84 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 16x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 16x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 16x + x2 = 0 + 84 16x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 16x + x2 = 84 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 = 84 + 64 Reorder the terms: 64 + 16x + x2 = 84 + 64 Combine like terms: 84 + 64 = 148 64 + 16x + x2 = 148 Factor a perfect square on the left side: (x + 8)(x + 8) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (x + 8) equal to 12.165525061 and -12.165525061.Subproblem 1
x + 8 = 12.165525061 Simplifying x + 8 = 12.165525061 Reorder the terms: 8 + x = 12.165525061 Solving 8 + x = 12.165525061 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 = 12.165525061 + -8 Combine like terms: 8 + -8 = 0 0 + x = 12.165525061 + -8 x = 12.165525061 + -8 Combine like terms: 12.165525061 + -8 = 4.165525061 x = 4.165525061 Simplifying x = 4.165525061Subproblem 2
x + 8 = -12.165525061 Simplifying x + 8 = -12.165525061 Reorder the terms: 8 + x = -12.165525061 Solving 8 + x = -12.165525061 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 = -12.165525061 + -8 Combine like terms: 8 + -8 = 0 0 + x = -12.165525061 + -8 x = -12.165525061 + -8 Combine like terms: -12.165525061 + -8 = -20.165525061 x = -20.165525061 Simplifying x = -20.165525061Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.165525061, -20.165525061}
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