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Simplifying 121x2 + -44x + 4 = 90 Reorder the terms: 4 + -44x + 121x2 = 90 Solving 4 + -44x + 121x2 = 90 Solving for variable 'x'. Reorder the terms: 4 + -90 + -44x + 121x2 = 90 + -90 Combine like terms: 4 + -90 = -86 -86 + -44x + 121x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -86 + -44x + 121x2 = 0 Begin completing the square. Divide all terms by 121 the coefficient of the squared term: Divide each side by '121'. -0.7107438017 + -0.3636363636x + x2 = 0 Move the constant term to the right: Add '0.7107438017' to each side of the equation. -0.7107438017 + -0.3636363636x + 0.7107438017 + x2 = 0 + 0.7107438017 Reorder the terms: -0.7107438017 + 0.7107438017 + -0.3636363636x + x2 = 0 + 0.7107438017 Combine like terms: -0.7107438017 + 0.7107438017 = 0.0000000000 0.0000000000 + -0.3636363636x + x2 = 0 + 0.7107438017 -0.3636363636x + x2 = 0 + 0.7107438017 Combine like terms: 0 + 0.7107438017 = 0.7107438017 -0.3636363636x + x2 = 0.7107438017 The x term is -0.3636363636x. Take half its coefficient (-0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. -0.3636363636x + 0.03305785123 + x2 = 0.7107438017 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636x + x2 = 0.7107438017 + 0.03305785123 Combine like terms: 0.7107438017 + 0.03305785123 = 0.74380165293 0.03305785123 + -0.3636363636x + x2 = 0.74380165293 Factor a perfect square on the left side: (x + -0.1818181818)(x + -0.1818181818) = 0.74380165293 Calculate the square root of the right side: 0.862439362 Break this problem into two subproblems by setting (x + -0.1818181818) equal to 0.862439362 and -0.862439362.Subproblem 1
x + -0.1818181818 = 0.862439362 Simplifying x + -0.1818181818 = 0.862439362 Reorder the terms: -0.1818181818 + x = 0.862439362 Solving -0.1818181818 + x = 0.862439362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = 0.862439362 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = 0.862439362 + 0.1818181818 x = 0.862439362 + 0.1818181818 Combine like terms: 0.862439362 + 0.1818181818 = 1.0442575438 x = 1.0442575438 Simplifying x = 1.0442575438Subproblem 2
x + -0.1818181818 = -0.862439362 Simplifying x + -0.1818181818 = -0.862439362 Reorder the terms: -0.1818181818 + x = -0.862439362 Solving -0.1818181818 + x = -0.862439362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = -0.862439362 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = -0.862439362 + 0.1818181818 x = -0.862439362 + 0.1818181818 Combine like terms: -0.862439362 + 0.1818181818 = -0.6806211802 x = -0.6806211802 Simplifying x = -0.6806211802Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0442575438, -0.6806211802}
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