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Simplifying x2 + 20x + 75 = 69 Reorder the terms: 75 + 20x + x2 = 69 Solving 75 + 20x + x2 = 69 Solving for variable 'x'. Reorder the terms: 75 + -69 + 20x + x2 = 69 + -69 Combine like terms: 75 + -69 = 6 6 + 20x + x2 = 69 + -69 Combine like terms: 69 + -69 = 0 6 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 20x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 20x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 20x + x2 = 0 + -6 20x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 20x + x2 = -6 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 = -6 + 100 Reorder the terms: 100 + 20x + x2 = -6 + 100 Combine like terms: -6 + 100 = 94 100 + 20x + x2 = 94 Factor a perfect square on the left side: (x + 10)(x + 10) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + 10) equal to 9.695359715 and -9.695359715.Subproblem 1
x + 10 = 9.695359715 Simplifying x + 10 = 9.695359715 Reorder the terms: 10 + x = 9.695359715 Solving 10 + x = 9.695359715 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 = 9.695359715 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.695359715 + -10 x = 9.695359715 + -10 Combine like terms: 9.695359715 + -10 = -0.304640285 x = -0.304640285 Simplifying x = -0.304640285Subproblem 2
x + 10 = -9.695359715 Simplifying x + 10 = -9.695359715 Reorder the terms: 10 + x = -9.695359715 Solving 10 + x = -9.695359715 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 = -9.695359715 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.695359715 + -10 x = -9.695359715 + -10 Combine like terms: -9.695359715 + -10 = -19.695359715 x = -19.695359715 Simplifying x = -19.695359715Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.304640285, -19.695359715}
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