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Simplifying 3x + x2 + -12x + 11 = 220 Reorder the terms: 11 + 3x + -12x + x2 = 220 Combine like terms: 3x + -12x = -9x 11 + -9x + x2 = 220 Solving 11 + -9x + x2 = 220 Solving for variable 'x'. Reorder the terms: 11 + -220 + -9x + x2 = 220 + -220 Combine like terms: 11 + -220 = -209 -209 + -9x + x2 = 220 + -220 Combine like terms: 220 + -220 = 0 -209 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '209' to each side of the equation. -209 + -9x + 209 + x2 = 0 + 209 Reorder the terms: -209 + 209 + -9x + x2 = 0 + 209 Combine like terms: -209 + 209 = 0 0 + -9x + x2 = 0 + 209 -9x + x2 = 0 + 209 Combine like terms: 0 + 209 = 209 -9x + x2 = 209 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 209 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 209 + 20.25 Combine like terms: 209 + 20.25 = 229.25 20.25 + -9x + x2 = 229.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 229.25 Calculate the square root of the right side: 15.14100393 Break this problem into two subproblems by setting (x + -4.5) equal to 15.14100393 and -15.14100393.Subproblem 1
x + -4.5 = 15.14100393 Simplifying x + -4.5 = 15.14100393 Reorder the terms: -4.5 + x = 15.14100393 Solving -4.5 + x = 15.14100393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 15.14100393 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 15.14100393 + 4.5 x = 15.14100393 + 4.5 Combine like terms: 15.14100393 + 4.5 = 19.64100393 x = 19.64100393 Simplifying x = 19.64100393Subproblem 2
x + -4.5 = -15.14100393 Simplifying x + -4.5 = -15.14100393 Reorder the terms: -4.5 + x = -15.14100393 Solving -4.5 + x = -15.14100393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -15.14100393 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -15.14100393 + 4.5 x = -15.14100393 + 4.5 Combine like terms: -15.14100393 + 4.5 = -10.64100393 x = -10.64100393 Simplifying x = -10.64100393Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.64100393, -10.64100393}
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