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Simplifying x2 + -10x + -86 = 0 Reorder the terms: -86 + -10x + x2 = 0 Solving -86 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '86' to each side of the equation. -86 + -10x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + -10x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + -10x + x2 = 0 + 86 -10x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 -10x + x2 = 86 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 86 + 25 Reorder the terms: 25 + -10x + x2 = 86 + 25 Combine like terms: 86 + 25 = 111 25 + -10x + x2 = 111 Factor a perfect square on the left side: (x + -5)(x + -5) = 111 Calculate the square root of the right side: 10.535653753 Break this problem into two subproblems by setting (x + -5) equal to 10.535653753 and -10.535653753.Subproblem 1
x + -5 = 10.535653753 Simplifying x + -5 = 10.535653753 Reorder the terms: -5 + x = 10.535653753 Solving -5 + x = 10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 10.535653753 + 5 Combine like terms: -5 + 5 = 0 0 + x = 10.535653753 + 5 x = 10.535653753 + 5 Combine like terms: 10.535653753 + 5 = 15.535653753 x = 15.535653753 Simplifying x = 15.535653753Subproblem 2
x + -5 = -10.535653753 Simplifying x + -5 = -10.535653753 Reorder the terms: -5 + x = -10.535653753 Solving -5 + x = -10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -10.535653753 + 5 Combine like terms: -5 + 5 = 0 0 + x = -10.535653753 + 5 x = -10.535653753 + 5 Combine like terms: -10.535653753 + 5 = -5.535653753 x = -5.535653753 Simplifying x = -5.535653753Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.535653753, -5.535653753}
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