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Simplifying x2 + -12x + 11 = 220 Reorder the terms: 11 + -12x + x2 = 220 Solving 11 + -12x + x2 = 220 Solving for variable 'x'. Reorder the terms: 11 + -220 + -12x + x2 = 220 + -220 Combine like terms: 11 + -220 = -209 -209 + -12x + x2 = 220 + -220 Combine like terms: 220 + -220 = 0 -209 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '209' to each side of the equation. -209 + -12x + 209 + x2 = 0 + 209 Reorder the terms: -209 + 209 + -12x + x2 = 0 + 209 Combine like terms: -209 + 209 = 0 0 + -12x + x2 = 0 + 209 -12x + x2 = 0 + 209 Combine like terms: 0 + 209 = 209 -12x + x2 = 209 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 = 209 + 36 Reorder the terms: 36 + -12x + x2 = 209 + 36 Combine like terms: 209 + 36 = 245 36 + -12x + x2 = 245 Factor a perfect square on the left side: (x + -6)(x + -6) = 245 Calculate the square root of the right side: 15.652475842 Break this problem into two subproblems by setting (x + -6) equal to 15.652475842 and -15.652475842.Subproblem 1
x + -6 = 15.652475842 Simplifying x + -6 = 15.652475842 Reorder the terms: -6 + x = 15.652475842 Solving -6 + x = 15.652475842 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 = 15.652475842 + 6 Combine like terms: -6 + 6 = 0 0 + x = 15.652475842 + 6 x = 15.652475842 + 6 Combine like terms: 15.652475842 + 6 = 21.652475842 x = 21.652475842 Simplifying x = 21.652475842Subproblem 2
x + -6 = -15.652475842 Simplifying x + -6 = -15.652475842 Reorder the terms: -6 + x = -15.652475842 Solving -6 + x = -15.652475842 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 = -15.652475842 + 6 Combine like terms: -6 + 6 = 0 0 + x = -15.652475842 + 6 x = -15.652475842 + 6 Combine like terms: -15.652475842 + 6 = -9.652475842 x = -9.652475842 Simplifying x = -9.652475842Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.652475842, -9.652475842}
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