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Simplifying x2 + 2x = 5625 Reorder the terms: 2x + x2 = 5625 Solving 2x + x2 = 5625 Solving for variable 'x'. Reorder the terms: -5625 + 2x + x2 = 5625 + -5625 Combine like terms: 5625 + -5625 = 0 -5625 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5625' to each side of the equation. -5625 + 2x + 5625 + x2 = 0 + 5625 Reorder the terms: -5625 + 5625 + 2x + x2 = 0 + 5625 Combine like terms: -5625 + 5625 = 0 0 + 2x + x2 = 0 + 5625 2x + x2 = 0 + 5625 Combine like terms: 0 + 5625 = 5625 2x + x2 = 5625 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 = 5625 + 1 Reorder the terms: 1 + 2x + x2 = 5625 + 1 Combine like terms: 5625 + 1 = 5626 1 + 2x + x2 = 5626 Factor a perfect square on the left side: (x + 1)(x + 1) = 5626 Calculate the square root of the right side: 75.00666637 Break this problem into two subproblems by setting (x + 1) equal to 75.00666637 and -75.00666637.Subproblem 1
x + 1 = 75.00666637 Simplifying x + 1 = 75.00666637 Reorder the terms: 1 + x = 75.00666637 Solving 1 + x = 75.00666637 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 = 75.00666637 + -1 Combine like terms: 1 + -1 = 0 0 + x = 75.00666637 + -1 x = 75.00666637 + -1 Combine like terms: 75.00666637 + -1 = 74.00666637 x = 74.00666637 Simplifying x = 74.00666637Subproblem 2
x + 1 = -75.00666637 Simplifying x + 1 = -75.00666637 Reorder the terms: 1 + x = -75.00666637 Solving 1 + x = -75.00666637 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 = -75.00666637 + -1 Combine like terms: 1 + -1 = 0 0 + x = -75.00666637 + -1 x = -75.00666637 + -1 Combine like terms: -75.00666637 + -1 = -76.00666637 x = -76.00666637 Simplifying x = -76.00666637Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.00666637, -76.00666637}
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