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Simplifying x2 + 2x + -930 = 0 Reorder the terms: -930 + 2x + x2 = 0 Solving -930 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '930' to each side of the equation. -930 + 2x + 930 + x2 = 0 + 930 Reorder the terms: -930 + 930 + 2x + x2 = 0 + 930 Combine like terms: -930 + 930 = 0 0 + 2x + x2 = 0 + 930 2x + x2 = 0 + 930 Combine like terms: 0 + 930 = 930 2x + x2 = 930 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 = 930 + 1 Reorder the terms: 1 + 2x + x2 = 930 + 1 Combine like terms: 930 + 1 = 931 1 + 2x + x2 = 931 Factor a perfect square on the left side: (x + 1)(x + 1) = 931 Calculate the square root of the right side: 30.512292605 Break this problem into two subproblems by setting (x + 1) equal to 30.512292605 and -30.512292605.Subproblem 1
x + 1 = 30.512292605 Simplifying x + 1 = 30.512292605 Reorder the terms: 1 + x = 30.512292605 Solving 1 + x = 30.512292605 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 = 30.512292605 + -1 Combine like terms: 1 + -1 = 0 0 + x = 30.512292605 + -1 x = 30.512292605 + -1 Combine like terms: 30.512292605 + -1 = 29.512292605 x = 29.512292605 Simplifying x = 29.512292605Subproblem 2
x + 1 = -30.512292605 Simplifying x + 1 = -30.512292605 Reorder the terms: 1 + x = -30.512292605 Solving 1 + x = -30.512292605 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 = -30.512292605 + -1 Combine like terms: 1 + -1 = 0 0 + x = -30.512292605 + -1 x = -30.512292605 + -1 Combine like terms: -30.512292605 + -1 = -31.512292605 x = -31.512292605 Simplifying x = -31.512292605Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.512292605, -31.512292605}
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