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Simplifying 18x2 + 8x + -8 = 0 Reorder the terms: -8 + 8x + 18x2 = 0 Solving -8 + 8x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 4x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 4x + 9x2)' equal to zero and attempt to solve: Simplifying -4 + 4x + 9x2 = 0 Solving -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}Solution
x = {0.4805061468, -0.9249505912}
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