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Simplifying 6x2 + 3x2 + -4x + -8 = 0 Reorder the terms: -8 + -4x + 6x2 + 3x2 = 0 Combine like terms: 6x2 + 3x2 = 9x2 -8 + -4x + 9x2 = 0 Solving -8 + -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'. -0.8888888889 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.4444444444x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.4444444444x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.4444444444x + x2 = 0 + 0.8888888889 -0.4444444444x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.4444444444x + x2 = 0.8888888889 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 = 0.8888888889 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 0.8888888889 + 0.04938271604 Combine like terms: 0.8888888889 + 0.04938271604 = 0.93827160494 0.04938271604 + -0.4444444444x + x2 = 0.93827160494 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 0.93827160494 Calculate the square root of the right side: 0.96864421 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 0.96864421 and -0.96864421.Subproblem 1
x + -0.2222222222 = 0.96864421 Simplifying x + -0.2222222222 = 0.96864421 Reorder the terms: -0.2222222222 + x = 0.96864421 Solving -0.2222222222 + x = 0.96864421 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 = 0.96864421 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 0.96864421 + 0.2222222222 x = 0.96864421 + 0.2222222222 Combine like terms: 0.96864421 + 0.2222222222 = 1.1908664322 x = 1.1908664322 Simplifying x = 1.1908664322Subproblem 2
x + -0.2222222222 = -0.96864421 Simplifying x + -0.2222222222 = -0.96864421 Reorder the terms: -0.2222222222 + x = -0.96864421 Solving -0.2222222222 + x = -0.96864421 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 = -0.96864421 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -0.96864421 + 0.2222222222 x = -0.96864421 + 0.2222222222 Combine like terms: -0.96864421 + 0.2222222222 = -0.7464219878 x = -0.7464219878 Simplifying x = -0.7464219878Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1908664322, -0.7464219878}
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