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Simplifying x2 + 8x + -43 = 0 Reorder the terms: -43 + 8x + x2 = 0 Solving -43 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 8x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + 8x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 8x + x2 = 0 + 43 8x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 8x + x2 = 43 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 43 + 16 Reorder the terms: 16 + 8x + x2 = 43 + 16 Combine like terms: 43 + 16 = 59 16 + 8x + x2 = 59 Factor a perfect square on the left side: (x + 4)(x + 4) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + 4) equal to 7.681145748 and -7.681145748.Subproblem 1
x + 4 = 7.681145748 Simplifying x + 4 = 7.681145748 Reorder the terms: 4 + x = 7.681145748 Solving 4 + x = 7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 7.681145748 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.681145748 + -4 x = 7.681145748 + -4 Combine like terms: 7.681145748 + -4 = 3.681145748 x = 3.681145748 Simplifying x = 3.681145748Subproblem 2
x + 4 = -7.681145748 Simplifying x + 4 = -7.681145748 Reorder the terms: 4 + x = -7.681145748 Solving 4 + x = -7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -7.681145748 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.681145748 + -4 x = -7.681145748 + -4 Combine like terms: -7.681145748 + -4 = -11.681145748 x = -11.681145748 Simplifying x = -11.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.681145748, -11.681145748}
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