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Simplifying x2 + 2x = 1624 Reorder the terms: 2x + x2 = 1624 Solving 2x + x2 = 1624 Solving for variable 'x'. Reorder the terms: -1624 + 2x + x2 = 1624 + -1624 Combine like terms: 1624 + -1624 = 0 -1624 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1624' to each side of the equation. -1624 + 2x + 1624 + x2 = 0 + 1624 Reorder the terms: -1624 + 1624 + 2x + x2 = 0 + 1624 Combine like terms: -1624 + 1624 = 0 0 + 2x + x2 = 0 + 1624 2x + x2 = 0 + 1624 Combine like terms: 0 + 1624 = 1624 2x + x2 = 1624 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 = 1624 + 1 Reorder the terms: 1 + 2x + x2 = 1624 + 1 Combine like terms: 1624 + 1 = 1625 1 + 2x + x2 = 1625 Factor a perfect square on the left side: (x + 1)(x + 1) = 1625 Calculate the square root of the right side: 40.311288741 Break this problem into two subproblems by setting (x + 1) equal to 40.311288741 and -40.311288741.Subproblem 1
x + 1 = 40.311288741 Simplifying x + 1 = 40.311288741 Reorder the terms: 1 + x = 40.311288741 Solving 1 + x = 40.311288741 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 = 40.311288741 + -1 Combine like terms: 1 + -1 = 0 0 + x = 40.311288741 + -1 x = 40.311288741 + -1 Combine like terms: 40.311288741 + -1 = 39.311288741 x = 39.311288741 Simplifying x = 39.311288741Subproblem 2
x + 1 = -40.311288741 Simplifying x + 1 = -40.311288741 Reorder the terms: 1 + x = -40.311288741 Solving 1 + x = -40.311288741 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 = -40.311288741 + -1 Combine like terms: 1 + -1 = 0 0 + x = -40.311288741 + -1 x = -40.311288741 + -1 Combine like terms: -40.311288741 + -1 = -41.311288741 x = -41.311288741 Simplifying x = -41.311288741Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.311288741, -41.311288741}
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