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Simplifying (x + 20)(x + 10) = 90 Reorder the terms: (20 + x)(x + 10) = 90 Reorder the terms: (20 + x)(10 + x) = 90 Multiply (20 + x) * (10 + x) (20(10 + x) + x(10 + x)) = 90 ((10 * 20 + x * 20) + x(10 + x)) = 90 ((200 + 20x) + x(10 + x)) = 90 (200 + 20x + (10 * x + x * x)) = 90 (200 + 20x + (10x + x2)) = 90 Combine like terms: 20x + 10x = 30x (200 + 30x + x2) = 90 Solving 200 + 30x + x2 = 90 Solving for variable 'x'. Reorder the terms: 200 + -90 + 30x + x2 = 90 + -90 Combine like terms: 200 + -90 = 110 110 + 30x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 110 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-110' to each side of the equation. 110 + 30x + -110 + x2 = 0 + -110 Reorder the terms: 110 + -110 + 30x + x2 = 0 + -110 Combine like terms: 110 + -110 = 0 0 + 30x + x2 = 0 + -110 30x + x2 = 0 + -110 Combine like terms: 0 + -110 = -110 30x + x2 = -110 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -110 + 225 Reorder the terms: 225 + 30x + x2 = -110 + 225 Combine like terms: -110 + 225 = 115 225 + 30x + x2 = 115 Factor a perfect square on the left side: (x + 15)(x + 15) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x + 15) equal to 10.723805295 and -10.723805295.Subproblem 1
x + 15 = 10.723805295 Simplifying x + 15 = 10.723805295 Reorder the terms: 15 + x = 10.723805295 Solving 15 + x = 10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 10.723805295 + -15 Combine like terms: 15 + -15 = 0 0 + x = 10.723805295 + -15 x = 10.723805295 + -15 Combine like terms: 10.723805295 + -15 = -4.276194705 x = -4.276194705 Simplifying x = -4.276194705Subproblem 2
x + 15 = -10.723805295 Simplifying x + 15 = -10.723805295 Reorder the terms: 15 + x = -10.723805295 Solving 15 + x = -10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -10.723805295 + -15 Combine like terms: 15 + -15 = 0 0 + x = -10.723805295 + -15 x = -10.723805295 + -15 Combine like terms: -10.723805295 + -15 = -25.723805295 x = -25.723805295 Simplifying x = -25.723805295Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.276194705, -25.723805295}
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