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Simplifying 0.33x2 + 8x + -3 = 0 Reorder the terms: -3 + 8x + 0.33x2 = 0 Solving -3 + 8x + 0.33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.33 the coefficient of the squared term: Divide each side by '0.33'. -9.090909091 + 24.24242424x + x2 = 0 Move the constant term to the right: Add '9.090909091' to each side of the equation. -9.090909091 + 24.24242424x + 9.090909091 + x2 = 0 + 9.090909091 Reorder the terms: -9.090909091 + 9.090909091 + 24.24242424x + x2 = 0 + 9.090909091 Combine like terms: -9.090909091 + 9.090909091 = 0.000000000 0.000000000 + 24.24242424x + x2 = 0 + 9.090909091 24.24242424x + x2 = 0 + 9.090909091 Combine like terms: 0 + 9.090909091 = 9.090909091 24.24242424x + x2 = 9.090909091 The x term is 24.24242424x. Take half its coefficient (12.12121212). Square it (146.9237833) and add it to both sides. Add '146.9237833' to each side of the equation. 24.24242424x + 146.9237833 + x2 = 9.090909091 + 146.9237833 Reorder the terms: 146.9237833 + 24.24242424x + x2 = 9.090909091 + 146.9237833 Combine like terms: 9.090909091 + 146.9237833 = 156.014692391 146.9237833 + 24.24242424x + x2 = 156.014692391 Factor a perfect square on the left side: (x + 12.12121212)(x + 12.12121212) = 156.014692391 Calculate the square root of the right side: 12.490584149 Break this problem into two subproblems by setting (x + 12.12121212) equal to 12.490584149 and -12.490584149.Subproblem 1
x + 12.12121212 = 12.490584149 Simplifying x + 12.12121212 = 12.490584149 Reorder the terms: 12.12121212 + x = 12.490584149 Solving 12.12121212 + x = 12.490584149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.12121212' to each side of the equation. 12.12121212 + -12.12121212 + x = 12.490584149 + -12.12121212 Combine like terms: 12.12121212 + -12.12121212 = 0.00000000 0.00000000 + x = 12.490584149 + -12.12121212 x = 12.490584149 + -12.12121212 Combine like terms: 12.490584149 + -12.12121212 = 0.369372029 x = 0.369372029 Simplifying x = 0.369372029Subproblem 2
x + 12.12121212 = -12.490584149 Simplifying x + 12.12121212 = -12.490584149 Reorder the terms: 12.12121212 + x = -12.490584149 Solving 12.12121212 + x = -12.490584149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.12121212' to each side of the equation. 12.12121212 + -12.12121212 + x = -12.490584149 + -12.12121212 Combine like terms: 12.12121212 + -12.12121212 = 0.00000000 0.00000000 + x = -12.490584149 + -12.12121212 x = -12.490584149 + -12.12121212 Combine like terms: -12.490584149 + -12.12121212 = -24.611796269 x = -24.611796269 Simplifying x = -24.611796269Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.369372029, -24.611796269}
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