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Simplifying (x + 3)(x + 18) = 180 Reorder the terms: (3 + x)(x + 18) = 180 Reorder the terms: (3 + x)(18 + x) = 180 Multiply (3 + x) * (18 + x) (3(18 + x) + x(18 + x)) = 180 ((18 * 3 + x * 3) + x(18 + x)) = 180 ((54 + 3x) + x(18 + x)) = 180 (54 + 3x + (18 * x + x * x)) = 180 (54 + 3x + (18x + x2)) = 180 Combine like terms: 3x + 18x = 21x (54 + 21x + x2) = 180 Solving 54 + 21x + x2 = 180 Solving for variable 'x'. Reorder the terms: 54 + -180 + 21x + x2 = 180 + -180 Combine like terms: 54 + -180 = -126 -126 + 21x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -126 + 21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + 21x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + 21x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 21x + x2 = 0 + 126 21x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 21x + x2 = 126 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = 126 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 126 + 110.25 Combine like terms: 126 + 110.25 = 236.25 110.25 + 21x + x2 = 236.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 236.25 Calculate the square root of the right side: 15.370426149 Break this problem into two subproblems by setting (x + 10.5) equal to 15.370426149 and -15.370426149.Subproblem 1
x + 10.5 = 15.370426149 Simplifying x + 10.5 = 15.370426149 Reorder the terms: 10.5 + x = 15.370426149 Solving 10.5 + x = 15.370426149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 15.370426149 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 15.370426149 + -10.5 x = 15.370426149 + -10.5 Combine like terms: 15.370426149 + -10.5 = 4.870426149 x = 4.870426149 Simplifying x = 4.870426149Subproblem 2
x + 10.5 = -15.370426149 Simplifying x + 10.5 = -15.370426149 Reorder the terms: 10.5 + x = -15.370426149 Solving 10.5 + x = -15.370426149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -15.370426149 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -15.370426149 + -10.5 x = -15.370426149 + -10.5 Combine like terms: -15.370426149 + -10.5 = -25.870426149 x = -25.870426149 Simplifying x = -25.870426149Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.870426149, -25.870426149}
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