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Simplifying 88 + -1x2 = 114 + -12x Solving 88 + -1x2 = 114 + -12x Solving for variable 'x'. Reorder the terms: 88 + -114 + 12x + -1x2 = 114 + -12x + -114 + 12x Combine like terms: 88 + -114 = -26 -26 + 12x + -1x2 = 114 + -12x + -114 + 12x Reorder the terms: -26 + 12x + -1x2 = 114 + -114 + -12x + 12x Combine like terms: 114 + -114 = 0 -26 + 12x + -1x2 = 0 + -12x + 12x -26 + 12x + -1x2 = -12x + 12x Combine like terms: -12x + 12x = 0 -26 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 26 + -12x + x2 = 0 Move the constant term to the right: Add '-26' to each side of the equation. 26 + -12x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + -12x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -12x + x2 = 0 + -26 -12x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 -12x + x2 = -26 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -26 + 36 Reorder the terms: 36 + -12x + x2 = -26 + 36 Combine like terms: -26 + 36 = 10 36 + -12x + x2 = 10 Factor a perfect square on the left side: (x + -6)(x + -6) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -6) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -6 = 3.16227766 Simplifying x + -6 = 3.16227766 Reorder the terms: -6 + x = 3.16227766 Solving -6 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 3.16227766 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.16227766 + 6 x = 3.16227766 + 6 Combine like terms: 3.16227766 + 6 = 9.16227766 x = 9.16227766 Simplifying x = 9.16227766Subproblem 2
x + -6 = -3.16227766 Simplifying x + -6 = -3.16227766 Reorder the terms: -6 + x = -3.16227766 Solving -6 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -3.16227766 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.16227766 + 6 x = -3.16227766 + 6 Combine like terms: -3.16227766 + 6 = 2.83772234 x = 2.83772234 Simplifying x = 2.83772234Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.16227766, 2.83772234}
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