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Simplifying 9x2 + -4x + -4 = 0 Reorder the terms: -4 + -4x + 9x2 = 0 Solving -4 + -4x + 9x2 = 0 Solving for variable 'x'. 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 = 0.9249505912 x = 0.9249505912 Simplifying x = 0.9249505912Subproblem 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 = -0.4805061468 x = -0.4805061468 Simplifying x = -0.4805061468Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9249505912, -0.4805061468}
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