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Simplifying 2x + 5 = 9x2 + 6x + 1 Reorder the terms: 5 + 2x = 9x2 + 6x + 1 Reorder the terms: 5 + 2x = 1 + 6x + 9x2 Solving 5 + 2x = 1 + 6x + 9x2 Solving for variable 'x'. Reorder the terms: 5 + -1 + 2x + -6x + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2 Combine like terms: 5 + -1 = 4 4 + 2x + -6x + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2 Combine like terms: 2x + -6x = -4x 4 + -4x + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2 Reorder the terms: 4 + -4x + -9x2 = 1 + -1 + 6x + -6x + 9x2 + -9x2 Combine like terms: 1 + -1 = 0 4 + -4x + -9x2 = 0 + 6x + -6x + 9x2 + -9x2 4 + -4x + -9x2 = 6x + -6x + 9x2 + -9x2 Combine like terms: 6x + -6x = 0 4 + -4x + -9x2 = 0 + 9x2 + -9x2 4 + -4x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 4 + -4x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.4444444444 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 0.4444444444x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 0.4444444444x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 0.4444444444x + x2 = 0 + 0.4444444444 0.4444444444x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 0.4444444444x + x2 = 0.4444444444 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 0.4444444444 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 0.4444444444 + 0.04938271604 Combine like terms: 0.4444444444 + 0.04938271604 = 0.49382716044 0.04938271604 + 0.4444444444x + x2 = 0.49382716044 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 0.49382716044 Calculate the square root of the right side: 0.702728369 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 0.702728369 and -0.702728369.Subproblem 1
x + 0.2222222222 = 0.702728369 Simplifying x + 0.2222222222 = 0.702728369 Reorder the terms: 0.2222222222 + x = 0.702728369 Solving 0.2222222222 + x = 0.702728369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 0.702728369 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 0.702728369 + -0.2222222222 x = 0.702728369 + -0.2222222222 Combine like terms: 0.702728369 + -0.2222222222 = 0.4805061468 x = 0.4805061468 Simplifying x = 0.4805061468Subproblem 2
x + 0.2222222222 = -0.702728369 Simplifying x + 0.2222222222 = -0.702728369 Reorder the terms: 0.2222222222 + x = -0.702728369 Solving 0.2222222222 + x = -0.702728369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -0.702728369 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -0.702728369 + -0.2222222222 x = -0.702728369 + -0.2222222222 Combine like terms: -0.702728369 + -0.2222222222 = -0.9249505912 x = -0.9249505912 Simplifying x = -0.9249505912Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4805061468, -0.9249505912}
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