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Simplifying 9x2 + -34x + 7 = 0 Reorder the terms: 7 + -34x + 9x2 = 0 Solving 7 + -34x + 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'. 0.7777777778 + -3.777777778x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + -3.777777778x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + -3.777777778x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + -3.777777778x + x2 = 0 + -0.7777777778 -3.777777778x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 -3.777777778x + x2 = -0.7777777778 The x term is -3.777777778x. Take half its coefficient (-1.888888889). Square it (3.567901235) and add it to both sides. Add '3.567901235' to each side of the equation. -3.777777778x + 3.567901235 + x2 = -0.7777777778 + 3.567901235 Reorder the terms: 3.567901235 + -3.777777778x + x2 = -0.7777777778 + 3.567901235 Combine like terms: -0.7777777778 + 3.567901235 = 2.7901234572 3.567901235 + -3.777777778x + x2 = 2.7901234572 Factor a perfect square on the left side: (x + -1.888888889)(x + -1.888888889) = 2.7901234572 Calculate the square root of the right side: 1.670366264 Break this problem into two subproblems by setting (x + -1.888888889) equal to 1.670366264 and -1.670366264.Subproblem 1
x + -1.888888889 = 1.670366264 Simplifying x + -1.888888889 = 1.670366264 Reorder the terms: -1.888888889 + x = 1.670366264 Solving -1.888888889 + x = 1.670366264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x = 1.670366264 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = 1.670366264 + 1.888888889 x = 1.670366264 + 1.888888889 Combine like terms: 1.670366264 + 1.888888889 = 3.559255153 x = 3.559255153 Simplifying x = 3.559255153Subproblem 2
x + -1.888888889 = -1.670366264 Simplifying x + -1.888888889 = -1.670366264 Reorder the terms: -1.888888889 + x = -1.670366264 Solving -1.888888889 + x = -1.670366264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x = -1.670366264 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = -1.670366264 + 1.888888889 x = -1.670366264 + 1.888888889 Combine like terms: -1.670366264 + 1.888888889 = 0.218522625 x = 0.218522625 Simplifying x = 0.218522625Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.559255153, 0.218522625}
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