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Simplifying x2 = 11 + 12x Solving x2 = 11 + 12x Solving for variable 'x'. Reorder the terms: -11 + -12x + x2 = 11 + 12x + -11 + -12x Reorder the terms: -11 + -12x + x2 = 11 + -11 + 12x + -12x Combine like terms: 11 + -11 = 0 -11 + -12x + x2 = 0 + 12x + -12x -11 + -12x + x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -11 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -12x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -12x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -12x + x2 = 0 + 11 -12x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -12x + x2 = 11 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 = 11 + 36 Reorder the terms: 36 + -12x + x2 = 11 + 36 Combine like terms: 11 + 36 = 47 36 + -12x + x2 = 47 Factor a perfect square on the left side: (x + -6)(x + -6) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + -6) equal to 6.8556546 and -6.8556546.Subproblem 1
x + -6 = 6.8556546 Simplifying x + -6 = 6.8556546 Reorder the terms: -6 + x = 6.8556546 Solving -6 + x = 6.8556546 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 = 6.8556546 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.8556546 + 6 x = 6.8556546 + 6 Combine like terms: 6.8556546 + 6 = 12.8556546 x = 12.8556546 Simplifying x = 12.8556546Subproblem 2
x + -6 = -6.8556546 Simplifying x + -6 = -6.8556546 Reorder the terms: -6 + x = -6.8556546 Solving -6 + x = -6.8556546 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 = -6.8556546 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.8556546 + 6 x = -6.8556546 + 6 Combine like terms: -6.8556546 + 6 = -0.8556546 x = -0.8556546 Simplifying x = -0.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.8556546, -0.8556546}
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