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Simplifying 9x2 + 7x = 9 Reorder the terms: 7x + 9x2 = 9 Solving 7x + 9x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 7x + 9x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.7777777778x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.7777777778x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.7777777778x + x2 = 0 + 1 0.7777777778x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.7777777778x + x2 = 1 The x term is 0.7777777778x. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778x + 0.1512345679 + x2 = 1 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 1 + 0.1512345679 Combine like terms: 1 + 0.1512345679 = 1.1512345679 0.1512345679 + 0.7777777778x + x2 = 1.1512345679 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 1.1512345679 Calculate the square root of the right side: 1.072955995 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 1.072955995 and -1.072955995.Subproblem 1
x + 0.3888888889 = 1.072955995 Simplifying x + 0.3888888889 = 1.072955995 Reorder the terms: 0.3888888889 + x = 1.072955995 Solving 0.3888888889 + x = 1.072955995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = 1.072955995 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 1.072955995 + -0.3888888889 x = 1.072955995 + -0.3888888889 Combine like terms: 1.072955995 + -0.3888888889 = 0.6840671061 x = 0.6840671061 Simplifying x = 0.6840671061Subproblem 2
x + 0.3888888889 = -1.072955995 Simplifying x + 0.3888888889 = -1.072955995 Reorder the terms: 0.3888888889 + x = -1.072955995 Solving 0.3888888889 + x = -1.072955995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = -1.072955995 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -1.072955995 + -0.3888888889 x = -1.072955995 + -0.3888888889 Combine like terms: -1.072955995 + -0.3888888889 = -1.4618448839 x = -1.4618448839 Simplifying x = -1.4618448839Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6840671061, -1.4618448839}
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