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Simplifying x(x + 2) = 625 Reorder the terms: x(2 + x) = 625 (2 * x + x * x) = 625 (2x + x2) = 625 Solving 2x + x2 = 625 Solving for variable 'x'. Reorder the terms: -625 + 2x + x2 = 625 + -625 Combine like terms: 625 + -625 = 0 -625 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '625' to each side of the equation. -625 + 2x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + 2x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + 2x + x2 = 0 + 625 2x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 2x + x2 = 625 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 625 + 1 Reorder the terms: 1 + 2x + x2 = 625 + 1 Combine like terms: 625 + 1 = 626 1 + 2x + x2 = 626 Factor a perfect square on the left side: (x + 1)(x + 1) = 626 Calculate the square root of the right side: 25.019992006 Break this problem into two subproblems by setting (x + 1) equal to 25.019992006 and -25.019992006.Subproblem 1
x + 1 = 25.019992006 Simplifying x + 1 = 25.019992006 Reorder the terms: 1 + x = 25.019992006 Solving 1 + x = 25.019992006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 25.019992006 + -1 Combine like terms: 1 + -1 = 0 0 + x = 25.019992006 + -1 x = 25.019992006 + -1 Combine like terms: 25.019992006 + -1 = 24.019992006 x = 24.019992006 Simplifying x = 24.019992006Subproblem 2
x + 1 = -25.019992006 Simplifying x + 1 = -25.019992006 Reorder the terms: 1 + x = -25.019992006 Solving 1 + x = -25.019992006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -25.019992006 + -1 Combine like terms: 1 + -1 = 0 0 + x = -25.019992006 + -1 x = -25.019992006 + -1 Combine like terms: -25.019992006 + -1 = -26.019992006 x = -26.019992006 Simplifying x = -26.019992006Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.019992006, -26.019992006}
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