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Simplifying x(x + 10) = 528 Reorder the terms: x(10 + x) = 528 (10 * x + x * x) = 528 (10x + x2) = 528 Solving 10x + x2 = 528 Solving for variable 'x'. Reorder the terms: -528 + 10x + x2 = 528 + -528 Combine like terms: 528 + -528 = 0 -528 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '528' to each side of the equation. -528 + 10x + 528 + x2 = 0 + 528 Reorder the terms: -528 + 528 + 10x + x2 = 0 + 528 Combine like terms: -528 + 528 = 0 0 + 10x + x2 = 0 + 528 10x + x2 = 0 + 528 Combine like terms: 0 + 528 = 528 10x + x2 = 528 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 528 + 25 Reorder the terms: 25 + 10x + x2 = 528 + 25 Combine like terms: 528 + 25 = 553 25 + 10x + x2 = 553 Factor a perfect square on the left side: (x + 5)(x + 5) = 553 Calculate the square root of the right side: 23.515952033 Break this problem into two subproblems by setting (x + 5) equal to 23.515952033 and -23.515952033.Subproblem 1
x + 5 = 23.515952033 Simplifying x + 5 = 23.515952033 Reorder the terms: 5 + x = 23.515952033 Solving 5 + x = 23.515952033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 23.515952033 + -5 Combine like terms: 5 + -5 = 0 0 + x = 23.515952033 + -5 x = 23.515952033 + -5 Combine like terms: 23.515952033 + -5 = 18.515952033 x = 18.515952033 Simplifying x = 18.515952033Subproblem 2
x + 5 = -23.515952033 Simplifying x + 5 = -23.515952033 Reorder the terms: 5 + x = -23.515952033 Solving 5 + x = -23.515952033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -23.515952033 + -5 Combine like terms: 5 + -5 = 0 0 + x = -23.515952033 + -5 x = -23.515952033 + -5 Combine like terms: -23.515952033 + -5 = -28.515952033 x = -28.515952033 Simplifying x = -28.515952033Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.515952033, -28.515952033}
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