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Simplifying (39x * x) + -7x + -34 = 0 Multiply x * x (39x2) + -7x + -34 = 0 Reorder the terms: -34 + -7x + (39x2) = 0 Solving -34 + -7x + (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'. -0.8717948718 + -0.1794871795x + x2 = 0 Move the constant term to the right: Add '0.8717948718' to each side of the equation. -0.8717948718 + -0.1794871795x + 0.8717948718 + x2 = 0 + 0.8717948718 Reorder the terms: -0.8717948718 + 0.8717948718 + -0.1794871795x + x2 = 0 + 0.8717948718 Combine like terms: -0.8717948718 + 0.8717948718 = 0.0000000000 0.0000000000 + -0.1794871795x + x2 = 0 + 0.8717948718 -0.1794871795x + x2 = 0 + 0.8717948718 Combine like terms: 0 + 0.8717948718 = 0.8717948718 -0.1794871795x + x2 = 0.8717948718 The x term is -0.1794871795x. Take half its coefficient (-0.08974358975). Square it (0.008053911901) and add it to both sides. Add '0.008053911901' to each side of the equation. -0.1794871795x + 0.008053911901 + x2 = 0.8717948718 + 0.008053911901 Reorder the terms: 0.008053911901 + -0.1794871795x + x2 = 0.8717948718 + 0.008053911901 Combine like terms: 0.8717948718 + 0.008053911901 = 0.879848783701 0.008053911901 + -0.1794871795x + x2 = 0.879848783701 Factor a perfect square on the left side: ((x) + -0.08974358975)((x) + -0.08974358975) = 0.879848783701 Calculate the square root of the right side: 0.93800255 Break this problem into two subproblems by setting ((x) + -0.08974358975) equal to 0.93800255 and -0.93800255.Subproblem 1
(x) + -0.08974358975 = 0.93800255 Simplifying (x) + -0.08974358975 = 0.93800255 x + -0.08974358975 = 0.93800255 Reorder the terms: -0.08974358975 + x = 0.93800255 Solving -0.08974358975 + x = 0.93800255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08974358975' to each side of the equation. -0.08974358975 + 0.08974358975 + x = 0.93800255 + 0.08974358975 Combine like terms: -0.08974358975 + 0.08974358975 = 0.00000000000 0.00000000000 + x = 0.93800255 + 0.08974358975 x = 0.93800255 + 0.08974358975 Combine like terms: 0.93800255 + 0.08974358975 = 1.02774613975 x = 1.02774613975 Simplifying x = 1.02774613975Subproblem 2
(x) + -0.08974358975 = -0.93800255 Simplifying (x) + -0.08974358975 = -0.93800255 x + -0.08974358975 = -0.93800255 Reorder the terms: -0.08974358975 + x = -0.93800255 Solving -0.08974358975 + x = -0.93800255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08974358975' to each side of the equation. -0.08974358975 + 0.08974358975 + x = -0.93800255 + 0.08974358975 Combine like terms: -0.08974358975 + 0.08974358975 = 0.00000000000 0.00000000000 + x = -0.93800255 + 0.08974358975 x = -0.93800255 + 0.08974358975 Combine like terms: -0.93800255 + 0.08974358975 = -0.84825896025 x = -0.84825896025 Simplifying x = -0.84825896025Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.02774613975, -0.84825896025}
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