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Simplifying 9x2 + -4x + -64 = 0 Reorder the terms: -64 + -4x + 9x2 = 0 Solving -64 + -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'. -7.111111111 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '7.111111111' to each side of the equation. -7.111111111 + -0.4444444444x + 7.111111111 + x2 = 0 + 7.111111111 Reorder the terms: -7.111111111 + 7.111111111 + -0.4444444444x + x2 = 0 + 7.111111111 Combine like terms: -7.111111111 + 7.111111111 = 0.000000000 0.000000000 + -0.4444444444x + x2 = 0 + 7.111111111 -0.4444444444x + x2 = 0 + 7.111111111 Combine like terms: 0 + 7.111111111 = 7.111111111 -0.4444444444x + x2 = 7.111111111 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 = 7.111111111 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 7.111111111 + 0.04938271604 Combine like terms: 7.111111111 + 0.04938271604 = 7.16049382704 0.04938271604 + -0.4444444444x + x2 = 7.16049382704 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 7.16049382704 Calculate the square root of the right side: 2.675909906 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 2.675909906 and -2.675909906.Subproblem 1
x + -0.2222222222 = 2.675909906 Simplifying x + -0.2222222222 = 2.675909906 Reorder the terms: -0.2222222222 + x = 2.675909906 Solving -0.2222222222 + x = 2.675909906 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 = 2.675909906 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 2.675909906 + 0.2222222222 x = 2.675909906 + 0.2222222222 Combine like terms: 2.675909906 + 0.2222222222 = 2.8981321282 x = 2.8981321282 Simplifying x = 2.8981321282Subproblem 2
x + -0.2222222222 = -2.675909906 Simplifying x + -0.2222222222 = -2.675909906 Reorder the terms: -0.2222222222 + x = -2.675909906 Solving -0.2222222222 + x = -2.675909906 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 = -2.675909906 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -2.675909906 + 0.2222222222 x = -2.675909906 + 0.2222222222 Combine like terms: -2.675909906 + 0.2222222222 = -2.4536876838 x = -2.4536876838 Simplifying x = -2.4536876838Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8981321282, -2.4536876838}
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