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Simplifying x2 + -10x + -10x = 11 Reorder the terms: -10x + -10x + x2 = 11 Combine like terms: -10x + -10x = -20x -20x + x2 = 11 Solving -20x + x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -20x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -20x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -20x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -20x + x2 = 0 + 11 -20x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -20x + x2 = 11 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 11 + 100 Reorder the terms: 100 + -20x + x2 = 11 + 100 Combine like terms: 11 + 100 = 111 100 + -20x + x2 = 111 Factor a perfect square on the left side: (x + -10)(x + -10) = 111 Calculate the square root of the right side: 10.535653753 Break this problem into two subproblems by setting (x + -10) equal to 10.535653753 and -10.535653753.Subproblem 1
x + -10 = 10.535653753 Simplifying x + -10 = 10.535653753 Reorder the terms: -10 + x = 10.535653753 Solving -10 + x = 10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 10.535653753 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.535653753 + 10 x = 10.535653753 + 10 Combine like terms: 10.535653753 + 10 = 20.535653753 x = 20.535653753 Simplifying x = 20.535653753Subproblem 2
x + -10 = -10.535653753 Simplifying x + -10 = -10.535653753 Reorder the terms: -10 + x = -10.535653753 Solving -10 + x = -10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -10.535653753 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.535653753 + 10 x = -10.535653753 + 10 Combine like terms: -10.535653753 + 10 = -0.535653753 x = -0.535653753 Simplifying x = -0.535653753Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.535653753, -0.535653753}
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