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Simplifying x2 + -10x = 1 Reorder the terms: -10x + x2 = 1 Solving -10x + x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -10x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -10x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -10x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -10x + x2 = 0 + 1 -10x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -10x + x2 = 1 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 = 1 + 25 Reorder the terms: 25 + -10x + x2 = 1 + 25 Combine like terms: 1 + 25 = 26 25 + -10x + x2 = 26 Factor a perfect square on the left side: (x + -5)(x + -5) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + -5) equal to 5.099019514 and -5.099019514.Subproblem 1
x + -5 = 5.099019514 Simplifying x + -5 = 5.099019514 Reorder the terms: -5 + x = 5.099019514 Solving -5 + x = 5.099019514 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 = 5.099019514 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.099019514 + 5 x = 5.099019514 + 5 Combine like terms: 5.099019514 + 5 = 10.099019514 x = 10.099019514 Simplifying x = 10.099019514Subproblem 2
x + -5 = -5.099019514 Simplifying x + -5 = -5.099019514 Reorder the terms: -5 + x = -5.099019514 Solving -5 + x = -5.099019514 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 = -5.099019514 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.099019514 + 5 x = -5.099019514 + 5 Combine like terms: -5.099019514 + 5 = -0.099019514 x = -0.099019514 Simplifying x = -0.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.099019514, -0.099019514}
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