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Simplifying (x + 15)(x + 5) = 84 Reorder the terms: (15 + x)(x + 5) = 84 Reorder the terms: (15 + x)(5 + x) = 84 Multiply (15 + x) * (5 + x) (15(5 + x) + x(5 + x)) = 84 ((5 * 15 + x * 15) + x(5 + x)) = 84 ((75 + 15x) + x(5 + x)) = 84 (75 + 15x + (5 * x + x * x)) = 84 (75 + 15x + (5x + x2)) = 84 Combine like terms: 15x + 5x = 20x (75 + 20x + x2) = 84 Solving 75 + 20x + x2 = 84 Solving for variable 'x'. Reorder the terms: 75 + -84 + 20x + x2 = 84 + -84 Combine like terms: 75 + -84 = -9 -9 + 20x + x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -9 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 20x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 20x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 20x + x2 = 0 + 9 20x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 20x + x2 = 9 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 = 9 + 100 Reorder the terms: 100 + 20x + x2 = 9 + 100 Combine like terms: 9 + 100 = 109 100 + 20x + x2 = 109 Factor a perfect square on the left side: (x + 10)(x + 10) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + 10) equal to 10.440306509 and -10.440306509.Subproblem 1
x + 10 = 10.440306509 Simplifying x + 10 = 10.440306509 Reorder the terms: 10 + x = 10.440306509 Solving 10 + x = 10.440306509 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 = 10.440306509 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.440306509 + -10 x = 10.440306509 + -10 Combine like terms: 10.440306509 + -10 = 0.440306509 x = 0.440306509 Simplifying x = 0.440306509Subproblem 2
x + 10 = -10.440306509 Simplifying x + 10 = -10.440306509 Reorder the terms: 10 + x = -10.440306509 Solving 10 + x = -10.440306509 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 = -10.440306509 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.440306509 + -10 x = -10.440306509 + -10 Combine like terms: -10.440306509 + -10 = -20.440306509 x = -20.440306509 Simplifying x = -20.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.440306509, -20.440306509}
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