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Simplifying 110 = x2 + -2x Reorder the terms: 110 = -2x + x2 Solving 110 = -2x + x2 Solving for variable 'x'. Reorder the terms: 110 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 110 + 2x + -1x2 = 0 + x2 + -1x2 110 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 110 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -110 + -2x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + -2x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + -2x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + -2x + x2 = 0 + 110 -2x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 -2x + x2 = 110 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 110 + 1 Reorder the terms: 1 + -2x + x2 = 110 + 1 Combine like terms: 110 + 1 = 111 1 + -2x + x2 = 111 Factor a perfect square on the left side: (x + -1)(x + -1) = 111 Calculate the square root of the right side: 10.535653753 Break this problem into two subproblems by setting (x + -1) equal to 10.535653753 and -10.535653753.Subproblem 1
x + -1 = 10.535653753 Simplifying x + -1 = 10.535653753 Reorder the terms: -1 + x = 10.535653753 Solving -1 + x = 10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 10.535653753 + 1 Combine like terms: -1 + 1 = 0 0 + x = 10.535653753 + 1 x = 10.535653753 + 1 Combine like terms: 10.535653753 + 1 = 11.535653753 x = 11.535653753 Simplifying x = 11.535653753Subproblem 2
x + -1 = -10.535653753 Simplifying x + -1 = -10.535653753 Reorder the terms: -1 + x = -10.535653753 Solving -1 + x = -10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -10.535653753 + 1 Combine like terms: -1 + 1 = 0 0 + x = -10.535653753 + 1 x = -10.535653753 + 1 Combine like terms: -10.535653753 + 1 = -9.535653753 x = -9.535653753 Simplifying x = -9.535653753Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.535653753, -9.535653753}
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