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Simplifying x2 + 2x + -875 = 0 Reorder the terms: -875 + 2x + x2 = 0 Solving -875 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '875' to each side of the equation. -875 + 2x + 875 + x2 = 0 + 875 Reorder the terms: -875 + 875 + 2x + x2 = 0 + 875 Combine like terms: -875 + 875 = 0 0 + 2x + x2 = 0 + 875 2x + x2 = 0 + 875 Combine like terms: 0 + 875 = 875 2x + x2 = 875 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 = 875 + 1 Reorder the terms: 1 + 2x + x2 = 875 + 1 Combine like terms: 875 + 1 = 876 1 + 2x + x2 = 876 Factor a perfect square on the left side: (x + 1)(x + 1) = 876 Calculate the square root of the right side: 29.597297174 Break this problem into two subproblems by setting (x + 1) equal to 29.597297174 and -29.597297174.Subproblem 1
x + 1 = 29.597297174 Simplifying x + 1 = 29.597297174 Reorder the terms: 1 + x = 29.597297174 Solving 1 + x = 29.597297174 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 = 29.597297174 + -1 Combine like terms: 1 + -1 = 0 0 + x = 29.597297174 + -1 x = 29.597297174 + -1 Combine like terms: 29.597297174 + -1 = 28.597297174 x = 28.597297174 Simplifying x = 28.597297174Subproblem 2
x + 1 = -29.597297174 Simplifying x + 1 = -29.597297174 Reorder the terms: 1 + x = -29.597297174 Solving 1 + x = -29.597297174 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 = -29.597297174 + -1 Combine like terms: 1 + -1 = 0 0 + x = -29.597297174 + -1 x = -29.597297174 + -1 Combine like terms: -29.597297174 + -1 = -30.597297174 x = -30.597297174 Simplifying x = -30.597297174Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.597297174, -30.597297174}
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