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Simplifying X2 + -8X + -114 = 0 Reorder the terms: -114 + -8X + X2 = 0 Solving -114 + -8X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '114' to each side of the equation. -114 + -8X + 114 + X2 = 0 + 114 Reorder the terms: -114 + 114 + -8X + X2 = 0 + 114 Combine like terms: -114 + 114 = 0 0 + -8X + X2 = 0 + 114 -8X + X2 = 0 + 114 Combine like terms: 0 + 114 = 114 -8X + X2 = 114 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 = 114 + 16 Reorder the terms: 16 + -8X + X2 = 114 + 16 Combine like terms: 114 + 16 = 130 16 + -8X + X2 = 130 Factor a perfect square on the left side: (X + -4)(X + -4) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (X + -4) equal to 11.401754251 and -11.401754251.Subproblem 1
X + -4 = 11.401754251 Simplifying X + -4 = 11.401754251 Reorder the terms: -4 + X = 11.401754251 Solving -4 + X = 11.401754251 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 = 11.401754251 + 4 Combine like terms: -4 + 4 = 0 0 + X = 11.401754251 + 4 X = 11.401754251 + 4 Combine like terms: 11.401754251 + 4 = 15.401754251 X = 15.401754251 Simplifying X = 15.401754251Subproblem 2
X + -4 = -11.401754251 Simplifying X + -4 = -11.401754251 Reorder the terms: -4 + X = -11.401754251 Solving -4 + X = -11.401754251 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 = -11.401754251 + 4 Combine like terms: -4 + 4 = 0 0 + X = -11.401754251 + 4 X = -11.401754251 + 4 Combine like terms: -11.401754251 + 4 = -7.401754251 X = -7.401754251 Simplifying X = -7.401754251Solution
The solution to the problem is based on the solutions from the subproblems. X = {15.401754251, -7.401754251}
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