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Simplifying x2 + -12x + 11 = 1 Reorder the terms: 11 + -12x + x2 = 1 Solving 11 + -12x + x2 = 1 Solving for variable 'x'. Reorder the terms: 11 + -1 + -12x + x2 = 1 + -1 Combine like terms: 11 + -1 = 10 10 + -12x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 10 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -12x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -12x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -12x + x2 = 0 + -10 -12x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -12x + x2 = -10 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 = -10 + 36 Reorder the terms: 36 + -12x + x2 = -10 + 36 Combine like terms: -10 + 36 = 26 36 + -12x + x2 = 26 Factor a perfect square on the left side: (x + -6)(x + -6) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + -6) equal to 5.099019514 and -5.099019514.Subproblem 1
x + -6 = 5.099019514 Simplifying x + -6 = 5.099019514 Reorder the terms: -6 + x = 5.099019514 Solving -6 + x = 5.099019514 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 = 5.099019514 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.099019514 + 6 x = 5.099019514 + 6 Combine like terms: 5.099019514 + 6 = 11.099019514 x = 11.099019514 Simplifying x = 11.099019514Subproblem 2
x + -6 = -5.099019514 Simplifying x + -6 = -5.099019514 Reorder the terms: -6 + x = -5.099019514 Solving -6 + x = -5.099019514 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 = -5.099019514 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.099019514 + 6 x = -5.099019514 + 6 Combine like terms: -5.099019514 + 6 = 0.900980486 x = 0.900980486 Simplifying x = 0.900980486Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.099019514, 0.900980486}
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