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Simplifying x2 + -6x + -9 + -8 + -6x = 26 Reorder the terms: -9 + -8 + -6x + -6x + x2 = 26 Combine like terms: -9 + -8 = -17 -17 + -6x + -6x + x2 = 26 Combine like terms: -6x + -6x = -12x -17 + -12x + x2 = 26 Solving -17 + -12x + x2 = 26 Solving for variable 'x'. Reorder the terms: -17 + -26 + -12x + x2 = 26 + -26 Combine like terms: -17 + -26 = -43 -43 + -12x + x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -43 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -12x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + -12x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -12x + x2 = 0 + 43 -12x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 -12x + x2 = 43 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 = 43 + 36 Reorder the terms: 36 + -12x + x2 = 43 + 36 Combine like terms: 43 + 36 = 79 36 + -12x + x2 = 79 Factor a perfect square on the left side: (x + -6)(x + -6) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + -6) equal to 8.888194417 and -8.888194417.Subproblem 1
x + -6 = 8.888194417 Simplifying x + -6 = 8.888194417 Reorder the terms: -6 + x = 8.888194417 Solving -6 + x = 8.888194417 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 = 8.888194417 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.888194417 + 6 x = 8.888194417 + 6 Combine like terms: 8.888194417 + 6 = 14.888194417 x = 14.888194417 Simplifying x = 14.888194417Subproblem 2
x + -6 = -8.888194417 Simplifying x + -6 = -8.888194417 Reorder the terms: -6 + x = -8.888194417 Solving -6 + x = -8.888194417 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 = -8.888194417 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.888194417 + 6 x = -8.888194417 + 6 Combine like terms: -8.888194417 + 6 = -2.888194417 x = -2.888194417 Simplifying x = -2.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.888194417, -2.888194417}
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