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Simplifying x2 + -8x + 6 = 110 Reorder the terms: 6 + -8x + x2 = 110 Solving 6 + -8x + x2 = 110 Solving for variable 'x'. Reorder the terms: 6 + -110 + -8x + x2 = 110 + -110 Combine like terms: 6 + -110 = -104 -104 + -8x + x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -104 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + -8x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + -8x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + -8x + x2 = 0 + 104 -8x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 -8x + x2 = 104 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 = 104 + 16 Reorder the terms: 16 + -8x + x2 = 104 + 16 Combine like terms: 104 + 16 = 120 16 + -8x + x2 = 120 Factor a perfect square on the left side: (x + -4)(x + -4) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (x + -4) equal to 10.95445115 and -10.95445115.Subproblem 1
x + -4 = 10.95445115 Simplifying x + -4 = 10.95445115 Reorder the terms: -4 + x = 10.95445115 Solving -4 + x = 10.95445115 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 = 10.95445115 + 4 Combine like terms: -4 + 4 = 0 0 + x = 10.95445115 + 4 x = 10.95445115 + 4 Combine like terms: 10.95445115 + 4 = 14.95445115 x = 14.95445115 Simplifying x = 14.95445115Subproblem 2
x + -4 = -10.95445115 Simplifying x + -4 = -10.95445115 Reorder the terms: -4 + x = -10.95445115 Solving -4 + x = -10.95445115 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 = -10.95445115 + 4 Combine like terms: -4 + 4 = 0 0 + x = -10.95445115 + 4 x = -10.95445115 + 4 Combine like terms: -10.95445115 + 4 = -6.95445115 x = -6.95445115 Simplifying x = -6.95445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.95445115, -6.95445115}
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