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Simplifying x(x + 10) = 720 Reorder the terms: x(10 + x) = 720 (10 * x + x * x) = 720 (10x + x2) = 720 Solving 10x + x2 = 720 Solving for variable 'x'. Reorder the terms: -720 + 10x + x2 = 720 + -720 Combine like terms: 720 + -720 = 0 -720 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '720' to each side of the equation. -720 + 10x + 720 + x2 = 0 + 720 Reorder the terms: -720 + 720 + 10x + x2 = 0 + 720 Combine like terms: -720 + 720 = 0 0 + 10x + x2 = 0 + 720 10x + x2 = 0 + 720 Combine like terms: 0 + 720 = 720 10x + x2 = 720 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 = 720 + 25 Reorder the terms: 25 + 10x + x2 = 720 + 25 Combine like terms: 720 + 25 = 745 25 + 10x + x2 = 745 Factor a perfect square on the left side: (x + 5)(x + 5) = 745 Calculate the square root of the right side: 27.294688128 Break this problem into two subproblems by setting (x + 5) equal to 27.294688128 and -27.294688128.Subproblem 1
x + 5 = 27.294688128 Simplifying x + 5 = 27.294688128 Reorder the terms: 5 + x = 27.294688128 Solving 5 + x = 27.294688128 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 = 27.294688128 + -5 Combine like terms: 5 + -5 = 0 0 + x = 27.294688128 + -5 x = 27.294688128 + -5 Combine like terms: 27.294688128 + -5 = 22.294688128 x = 22.294688128 Simplifying x = 22.294688128Subproblem 2
x + 5 = -27.294688128 Simplifying x + 5 = -27.294688128 Reorder the terms: 5 + x = -27.294688128 Solving 5 + x = -27.294688128 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 = -27.294688128 + -5 Combine like terms: 5 + -5 = 0 0 + x = -27.294688128 + -5 x = -27.294688128 + -5 Combine like terms: -27.294688128 + -5 = -32.294688128 x = -32.294688128 Simplifying x = -32.294688128Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.294688128, -32.294688128}
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