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Simplifying -9x2 + -25x + 20 = 0 Reorder the terms: 20 + -25x + -9x2 = 0 Solving 20 + -25x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -2.222222222 + 2.777777778x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 2.777777778x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 2.777777778x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 2.777777778x + x2 = 0 + 2.222222222 2.777777778x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 2.777777778x + x2 = 2.222222222 The x term is 2.777777778x. Take half its coefficient (1.388888889). Square it (1.929012346) and add it to both sides. Add '1.929012346' to each side of the equation. 2.777777778x + 1.929012346 + x2 = 2.222222222 + 1.929012346 Reorder the terms: 1.929012346 + 2.777777778x + x2 = 2.222222222 + 1.929012346 Combine like terms: 2.222222222 + 1.929012346 = 4.151234568 1.929012346 + 2.777777778x + x2 = 4.151234568 Factor a perfect square on the left side: (x + 1.388888889)(x + 1.388888889) = 4.151234568 Calculate the square root of the right side: 2.037457869 Break this problem into two subproblems by setting (x + 1.388888889) equal to 2.037457869 and -2.037457869.Subproblem 1
x + 1.388888889 = 2.037457869 Simplifying x + 1.388888889 = 2.037457869 Reorder the terms: 1.388888889 + x = 2.037457869 Solving 1.388888889 + x = 2.037457869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.388888889' to each side of the equation. 1.388888889 + -1.388888889 + x = 2.037457869 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = 2.037457869 + -1.388888889 x = 2.037457869 + -1.388888889 Combine like terms: 2.037457869 + -1.388888889 = 0.64856898 x = 0.64856898 Simplifying x = 0.64856898Subproblem 2
x + 1.388888889 = -2.037457869 Simplifying x + 1.388888889 = -2.037457869 Reorder the terms: 1.388888889 + x = -2.037457869 Solving 1.388888889 + x = -2.037457869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.388888889' to each side of the equation. 1.388888889 + -1.388888889 + x = -2.037457869 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = -2.037457869 + -1.388888889 x = -2.037457869 + -1.388888889 Combine like terms: -2.037457869 + -1.388888889 = -3.426346758 x = -3.426346758 Simplifying x = -3.426346758Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.64856898, -3.426346758}
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