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Simplifying 33 = (10 + X)(16 + X) Multiply (10 + X) * (16 + X) 33 = (10(16 + X) + X(16 + X)) 33 = ((16 * 10 + X * 10) + X(16 + X)) 33 = ((160 + 10X) + X(16 + X)) 33 = (160 + 10X + (16 * X + X * X)) 33 = (160 + 10X + (16X + X2)) Combine like terms: 10X + 16X = 26X 33 = (160 + 26X + X2) Solving 33 = 160 + 26X + X2 Solving for variable 'X'. Combine like terms: 33 + -160 = -127 -127 + -26X + -1X2 = 160 + 26X + X2 + -160 + -26X + -1X2 Reorder the terms: -127 + -26X + -1X2 = 160 + -160 + 26X + -26X + X2 + -1X2 Combine like terms: 160 + -160 = 0 -127 + -26X + -1X2 = 0 + 26X + -26X + X2 + -1X2 -127 + -26X + -1X2 = 26X + -26X + X2 + -1X2 Combine like terms: 26X + -26X = 0 -127 + -26X + -1X2 = 0 + X2 + -1X2 -127 + -26X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -127 + -26X + -1X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(127 + 26X + X2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(127 + 26X + X2)' equal to zero and attempt to solve: Simplifying 127 + 26X + X2 = 0 Solving 127 + 26X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-127' to each side of the equation. 127 + 26X + -127 + X2 = 0 + -127 Reorder the terms: 127 + -127 + 26X + X2 = 0 + -127 Combine like terms: 127 + -127 = 0 0 + 26X + X2 = 0 + -127 26X + X2 = 0 + -127 Combine like terms: 0 + -127 = -127 26X + X2 = -127 The X term is 26X. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26X + 169 + X2 = -127 + 169 Reorder the terms: 169 + 26X + X2 = -127 + 169 Combine like terms: -127 + 169 = 42 169 + 26X + X2 = 42 Factor a perfect square on the left side: (X + 13)(X + 13) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (X + 13) equal to 6.480740698 and -6.480740698.Subproblem 1
X + 13 = 6.480740698 Simplifying X + 13 = 6.480740698 Reorder the terms: 13 + X = 6.480740698 Solving 13 + X = 6.480740698 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + X = 6.480740698 + -13 Combine like terms: 13 + -13 = 0 0 + X = 6.480740698 + -13 X = 6.480740698 + -13 Combine like terms: 6.480740698 + -13 = -6.519259302 X = -6.519259302 Simplifying X = -6.519259302Subproblem 2
X + 13 = -6.480740698 Simplifying X + 13 = -6.480740698 Reorder the terms: 13 + X = -6.480740698 Solving 13 + X = -6.480740698 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + X = -6.480740698 + -13 Combine like terms: 13 + -13 = 0 0 + X = -6.480740698 + -13 X = -6.480740698 + -13 Combine like terms: -6.480740698 + -13 = -19.480740698 X = -19.480740698 Simplifying X = -19.480740698Solution
The solution to the problem is based on the solutions from the subproblems. X = {-6.519259302, -19.480740698}Solution
X = {-6.519259302, -19.480740698}
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