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Simplifying x(x + 20) = 528 Reorder the terms: x(20 + x) = 528 (20 * x + x * x) = 528 (20x + x2) = 528 Solving 20x + x2 = 528 Solving for variable 'x'. Reorder the terms: -528 + 20x + x2 = 528 + -528 Combine like terms: 528 + -528 = 0 -528 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '528' to each side of the equation. -528 + 20x + 528 + x2 = 0 + 528 Reorder the terms: -528 + 528 + 20x + x2 = 0 + 528 Combine like terms: -528 + 528 = 0 0 + 20x + x2 = 0 + 528 20x + x2 = 0 + 528 Combine like terms: 0 + 528 = 528 20x + x2 = 528 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 = 528 + 100 Reorder the terms: 100 + 20x + x2 = 528 + 100 Combine like terms: 528 + 100 = 628 100 + 20x + x2 = 628 Factor a perfect square on the left side: (x + 10)(x + 10) = 628 Calculate the square root of the right side: 25.059928172 Break this problem into two subproblems by setting (x + 10) equal to 25.059928172 and -25.059928172.Subproblem 1
x + 10 = 25.059928172 Simplifying x + 10 = 25.059928172 Reorder the terms: 10 + x = 25.059928172 Solving 10 + x = 25.059928172 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 = 25.059928172 + -10 Combine like terms: 10 + -10 = 0 0 + x = 25.059928172 + -10 x = 25.059928172 + -10 Combine like terms: 25.059928172 + -10 = 15.059928172 x = 15.059928172 Simplifying x = 15.059928172Subproblem 2
x + 10 = -25.059928172 Simplifying x + 10 = -25.059928172 Reorder the terms: 10 + x = -25.059928172 Solving 10 + x = -25.059928172 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 = -25.059928172 + -10 Combine like terms: 10 + -10 = 0 0 + x = -25.059928172 + -10 x = -25.059928172 + -10 Combine like terms: -25.059928172 + -10 = -35.059928172 x = -35.059928172 Simplifying x = -35.059928172Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.059928172, -35.059928172}
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