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Simplifying 39x2 + -18x + -8 = 0 Reorder the terms: -8 + -18x + 39x2 = 0 Solving -8 + -18x + 39x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. -0.2051282051 + -0.4615384615x + x2 = 0 Move the constant term to the right: Add '0.2051282051' to each side of the equation. -0.2051282051 + -0.4615384615x + 0.2051282051 + x2 = 0 + 0.2051282051 Reorder the terms: -0.2051282051 + 0.2051282051 + -0.4615384615x + x2 = 0 + 0.2051282051 Combine like terms: -0.2051282051 + 0.2051282051 = 0.0000000000 0.0000000000 + -0.4615384615x + x2 = 0 + 0.2051282051 -0.4615384615x + x2 = 0 + 0.2051282051 Combine like terms: 0 + 0.2051282051 = 0.2051282051 -0.4615384615x + x2 = 0.2051282051 The x term is -0.4615384615x. Take half its coefficient (-0.2307692308). Square it (0.05325443788) and add it to both sides. Add '0.05325443788' to each side of the equation. -0.4615384615x + 0.05325443788 + x2 = 0.2051282051 + 0.05325443788 Reorder the terms: 0.05325443788 + -0.4615384615x + x2 = 0.2051282051 + 0.05325443788 Combine like terms: 0.2051282051 + 0.05325443788 = 0.25838264298 0.05325443788 + -0.4615384615x + x2 = 0.25838264298 Factor a perfect square on the left side: (x + -0.2307692308)(x + -0.2307692308) = 0.25838264298 Calculate the square root of the right side: 0.508313528 Break this problem into two subproblems by setting (x + -0.2307692308) equal to 0.508313528 and -0.508313528.Subproblem 1
x + -0.2307692308 = 0.508313528 Simplifying x + -0.2307692308 = 0.508313528 Reorder the terms: -0.2307692308 + x = 0.508313528 Solving -0.2307692308 + x = 0.508313528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2307692308' to each side of the equation. -0.2307692308 + 0.2307692308 + x = 0.508313528 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + x = 0.508313528 + 0.2307692308 x = 0.508313528 + 0.2307692308 Combine like terms: 0.508313528 + 0.2307692308 = 0.7390827588 x = 0.7390827588 Simplifying x = 0.7390827588Subproblem 2
x + -0.2307692308 = -0.508313528 Simplifying x + -0.2307692308 = -0.508313528 Reorder the terms: -0.2307692308 + x = -0.508313528 Solving -0.2307692308 + x = -0.508313528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2307692308' to each side of the equation. -0.2307692308 + 0.2307692308 + x = -0.508313528 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + x = -0.508313528 + 0.2307692308 x = -0.508313528 + 0.2307692308 Combine like terms: -0.508313528 + 0.2307692308 = -0.2775442972 x = -0.2775442972 Simplifying x = -0.2775442972Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7390827588, -0.2775442972}
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