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Simplifying -33x2 + -8x + 138 = 0 Reorder the terms: 138 + -8x + -33x2 = 0 Solving 138 + -8x + -33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -33 the coefficient of the squared term: Divide each side by '-33'. -4.181818182 + 0.2424242424x + x2 = 0 Move the constant term to the right: Add '4.181818182' to each side of the equation. -4.181818182 + 0.2424242424x + 4.181818182 + x2 = 0 + 4.181818182 Reorder the terms: -4.181818182 + 4.181818182 + 0.2424242424x + x2 = 0 + 4.181818182 Combine like terms: -4.181818182 + 4.181818182 = 0.000000000 0.000000000 + 0.2424242424x + x2 = 0 + 4.181818182 0.2424242424x + x2 = 0 + 4.181818182 Combine like terms: 0 + 4.181818182 = 4.181818182 0.2424242424x + x2 = 4.181818182 The x term is 0.2424242424x. Take half its coefficient (0.1212121212). Square it (0.01469237833) and add it to both sides. Add '0.01469237833' to each side of the equation. 0.2424242424x + 0.01469237833 + x2 = 4.181818182 + 0.01469237833 Reorder the terms: 0.01469237833 + 0.2424242424x + x2 = 4.181818182 + 0.01469237833 Combine like terms: 4.181818182 + 0.01469237833 = 4.19651056033 0.01469237833 + 0.2424242424x + x2 = 4.19651056033 Factor a perfect square on the left side: (x + 0.1212121212)(x + 0.1212121212) = 4.19651056033 Calculate the square root of the right side: 2.04853864 Break this problem into two subproblems by setting (x + 0.1212121212) equal to 2.04853864 and -2.04853864.Subproblem 1
x + 0.1212121212 = 2.04853864 Simplifying x + 0.1212121212 = 2.04853864 Reorder the terms: 0.1212121212 + x = 2.04853864 Solving 0.1212121212 + x = 2.04853864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1212121212' to each side of the equation. 0.1212121212 + -0.1212121212 + x = 2.04853864 + -0.1212121212 Combine like terms: 0.1212121212 + -0.1212121212 = 0.0000000000 0.0000000000 + x = 2.04853864 + -0.1212121212 x = 2.04853864 + -0.1212121212 Combine like terms: 2.04853864 + -0.1212121212 = 1.9273265188 x = 1.9273265188 Simplifying x = 1.9273265188Subproblem 2
x + 0.1212121212 = -2.04853864 Simplifying x + 0.1212121212 = -2.04853864 Reorder the terms: 0.1212121212 + x = -2.04853864 Solving 0.1212121212 + x = -2.04853864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1212121212' to each side of the equation. 0.1212121212 + -0.1212121212 + x = -2.04853864 + -0.1212121212 Combine like terms: 0.1212121212 + -0.1212121212 = 0.0000000000 0.0000000000 + x = -2.04853864 + -0.1212121212 x = -2.04853864 + -0.1212121212 Combine like terms: -2.04853864 + -0.1212121212 = -2.1697507612 x = -2.1697507612 Simplifying x = -2.1697507612Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9273265188, -2.1697507612}
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