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Simplifying x2 + 2x + -58 = 0 Reorder the terms: -58 + 2x + x2 = 0 Solving -58 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + 2x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + 2x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 2x + x2 = 0 + 58 2x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 2x + x2 = 58 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 = 58 + 1 Reorder the terms: 1 + 2x + x2 = 58 + 1 Combine like terms: 58 + 1 = 59 1 + 2x + x2 = 59 Factor a perfect square on the left side: (x + 1)(x + 1) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + 1) equal to 7.681145748 and -7.681145748.Subproblem 1
x + 1 = 7.681145748 Simplifying x + 1 = 7.681145748 Reorder the terms: 1 + x = 7.681145748 Solving 1 + x = 7.681145748 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 = 7.681145748 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.681145748 + -1 x = 7.681145748 + -1 Combine like terms: 7.681145748 + -1 = 6.681145748 x = 6.681145748 Simplifying x = 6.681145748Subproblem 2
x + 1 = -7.681145748 Simplifying x + 1 = -7.681145748 Reorder the terms: 1 + x = -7.681145748 Solving 1 + x = -7.681145748 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 = -7.681145748 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.681145748 + -1 x = -7.681145748 + -1 Combine like terms: -7.681145748 + -1 = -8.681145748 x = -8.681145748 Simplifying x = -8.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.681145748, -8.681145748}
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