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Simplifying (7x2) = 3x + 39 Reorder the terms: (7x2) = 39 + 3x Solving (7x2) = 39 + 3x Solving for variable 'x'. Reorder the terms: -39 + -3x + (7x2) = 39 + 3x + -39 + -3x Reorder the terms: -39 + -3x + (7x2) = 39 + -39 + 3x + -3x Combine like terms: 39 + -39 = 0 -39 + -3x + (7x2) = 0 + 3x + -3x -39 + -3x + (7x2) = 3x + -3x Combine like terms: 3x + -3x = 0 -39 + -3x + (7x2) = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.571428571 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '5.571428571' to each side of the equation. -5.571428571 + -0.4285714286x + 5.571428571 + x2 = 0 + 5.571428571 Reorder the terms: -5.571428571 + 5.571428571 + -0.4285714286x + x2 = 0 + 5.571428571 Combine like terms: -5.571428571 + 5.571428571 = 0.000000000 0.000000000 + -0.4285714286x + x2 = 0 + 5.571428571 -0.4285714286x + x2 = 0 + 5.571428571 Combine like terms: 0 + 5.571428571 = 5.571428571 -0.4285714286x + x2 = 5.571428571 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = 5.571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 5.571428571 + 0.04591836735 Combine like terms: 5.571428571 + 0.04591836735 = 5.61734693835 0.04591836735 + -0.4285714286x + x2 = 5.61734693835 Factor a perfect square on the left side: ((x) + -0.2142857143)((x) + -0.2142857143) = 5.61734693835 Calculate the square root of the right side: 2.370094289 Break this problem into two subproblems by setting ((x) + -0.2142857143) equal to 2.370094289 and -2.370094289.Subproblem 1
(x) + -0.2142857143 = 2.370094289 Simplifying (x) + -0.2142857143 = 2.370094289 x + -0.2142857143 = 2.370094289 Reorder the terms: -0.2142857143 + x = 2.370094289 Solving -0.2142857143 + x = 2.370094289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 2.370094289 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 2.370094289 + 0.2142857143 x = 2.370094289 + 0.2142857143 Combine like terms: 2.370094289 + 0.2142857143 = 2.5843800033 x = 2.5843800033 Simplifying x = 2.5843800033Subproblem 2
(x) + -0.2142857143 = -2.370094289 Simplifying (x) + -0.2142857143 = -2.370094289 x + -0.2142857143 = -2.370094289 Reorder the terms: -0.2142857143 + x = -2.370094289 Solving -0.2142857143 + x = -2.370094289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -2.370094289 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -2.370094289 + 0.2142857143 x = -2.370094289 + 0.2142857143 Combine like terms: -2.370094289 + 0.2142857143 = -2.1558085747 x = -2.1558085747 Simplifying x = -2.1558085747Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5843800033, -2.1558085747}
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