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Simplifying 18x2 + -3x + -24x + -4 = 0 Reorder the terms: -4 + -3x + -24x + 18x2 = 0 Combine like terms: -3x + -24x = -27x -4 + -27x + 18x2 = 0 Solving -4 + -27x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2222222222 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -1.5x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -1.5x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -1.5x + x2 = 0 + 0.2222222222 -1.5x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -1.5x + x2 = 0.2222222222 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.2222222222 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.2222222222 + 0.5625 Combine like terms: 0.2222222222 + 0.5625 = 0.7847222222 0.5625 + -1.5x + x2 = 0.7847222222 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.7847222222 Calculate the square root of the right side: 0.885845484 Break this problem into two subproblems by setting (x + -0.75) equal to 0.885845484 and -0.885845484.Subproblem 1
x + -0.75 = 0.885845484 Simplifying x + -0.75 = 0.885845484 Reorder the terms: -0.75 + x = 0.885845484 Solving -0.75 + x = 0.885845484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.885845484 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.885845484 + 0.75 x = 0.885845484 + 0.75 Combine like terms: 0.885845484 + 0.75 = 1.635845484 x = 1.635845484 Simplifying x = 1.635845484Subproblem 2
x + -0.75 = -0.885845484 Simplifying x + -0.75 = -0.885845484 Reorder the terms: -0.75 + x = -0.885845484 Solving -0.75 + x = -0.885845484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.885845484 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.885845484 + 0.75 x = -0.885845484 + 0.75 Combine like terms: -0.885845484 + 0.75 = -0.135845484 x = -0.135845484 Simplifying x = -0.135845484Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.635845484, -0.135845484}
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