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Simplifying 2x2 + 14x + 9 + -1x2 + 8x + 16 = 0 Reorder the terms: 9 + 16 + 14x + 8x + 2x2 + -1x2 = 0 Combine like terms: 9 + 16 = 25 25 + 14x + 8x + 2x2 + -1x2 = 0 Combine like terms: 14x + 8x = 22x 25 + 22x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 25 + 22x + 1x2 = 0 Solving 25 + 22x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 22x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + 22x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 22x + x2 = 0 + -25 22x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 22x + x2 = -25 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -25 + 121 Reorder the terms: 121 + 22x + x2 = -25 + 121 Combine like terms: -25 + 121 = 96 121 + 22x + x2 = 96 Factor a perfect square on the left side: (x + 11)(x + 11) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 11) equal to 9.797958971 and -9.797958971.Subproblem 1
x + 11 = 9.797958971 Simplifying x + 11 = 9.797958971 Reorder the terms: 11 + x = 9.797958971 Solving 11 + x = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 9.797958971 + -11 Combine like terms: 11 + -11 = 0 0 + x = 9.797958971 + -11 x = 9.797958971 + -11 Combine like terms: 9.797958971 + -11 = -1.202041029 x = -1.202041029 Simplifying x = -1.202041029Subproblem 2
x + 11 = -9.797958971 Simplifying x + 11 = -9.797958971 Reorder the terms: 11 + x = -9.797958971 Solving 11 + x = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -9.797958971 + -11 Combine like terms: 11 + -11 = 0 0 + x = -9.797958971 + -11 x = -9.797958971 + -11 Combine like terms: -9.797958971 + -11 = -20.797958971 x = -20.797958971 Simplifying x = -20.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.202041029, -20.797958971}
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