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Simplifying x2 + 8x + -89 = 0 Reorder the terms: -89 + 8x + x2 = 0 Solving -89 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 8x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + 8x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 8x + x2 = 0 + 89 8x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 8x + x2 = 89 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 = 89 + 16 Reorder the terms: 16 + 8x + x2 = 89 + 16 Combine like terms: 89 + 16 = 105 16 + 8x + x2 = 105 Factor a perfect square on the left side: (x + 4)(x + 4) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + 4) equal to 10.246950766 and -10.246950766.Subproblem 1
x + 4 = 10.246950766 Simplifying x + 4 = 10.246950766 Reorder the terms: 4 + x = 10.246950766 Solving 4 + x = 10.246950766 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 = 10.246950766 + -4 Combine like terms: 4 + -4 = 0 0 + x = 10.246950766 + -4 x = 10.246950766 + -4 Combine like terms: 10.246950766 + -4 = 6.246950766 x = 6.246950766 Simplifying x = 6.246950766Subproblem 2
x + 4 = -10.246950766 Simplifying x + 4 = -10.246950766 Reorder the terms: 4 + x = -10.246950766 Solving 4 + x = -10.246950766 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 = -10.246950766 + -4 Combine like terms: 4 + -4 = 0 0 + x = -10.246950766 + -4 x = -10.246950766 + -4 Combine like terms: -10.246950766 + -4 = -14.246950766 x = -14.246950766 Simplifying x = -14.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.246950766, -14.246950766}
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