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Simplifying x2 + 2x = 69 + 6x Reorder the terms: 2x + x2 = 69 + 6x Solving 2x + x2 = 69 + 6x Solving for variable 'x'. Reorder the terms: -69 + 2x + -6x + x2 = 69 + 6x + -69 + -6x Combine like terms: 2x + -6x = -4x -69 + -4x + x2 = 69 + 6x + -69 + -6x Reorder the terms: -69 + -4x + x2 = 69 + -69 + 6x + -6x Combine like terms: 69 + -69 = 0 -69 + -4x + x2 = 0 + 6x + -6x -69 + -4x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -69 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + -4x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + -4x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + -4x + x2 = 0 + 69 -4x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 -4x + x2 = 69 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 69 + 4 Reorder the terms: 4 + -4x + x2 = 69 + 4 Combine like terms: 69 + 4 = 73 4 + -4x + x2 = 73 Factor a perfect square on the left side: (x + -2)(x + -2) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + -2) equal to 8.544003745 and -8.544003745.Subproblem 1
x + -2 = 8.544003745 Simplifying x + -2 = 8.544003745 Reorder the terms: -2 + x = 8.544003745 Solving -2 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 8.544003745 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.544003745 + 2 x = 8.544003745 + 2 Combine like terms: 8.544003745 + 2 = 10.544003745 x = 10.544003745 Simplifying x = 10.544003745Subproblem 2
x + -2 = -8.544003745 Simplifying x + -2 = -8.544003745 Reorder the terms: -2 + x = -8.544003745 Solving -2 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -8.544003745 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.544003745 + 2 x = -8.544003745 + 2 Combine like terms: -8.544003745 + 2 = -6.544003745 x = -6.544003745 Simplifying x = -6.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.544003745, -6.544003745}
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