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Simplifying 5 + -1(9x2 + 7x) = 0 Reorder the terms: 5 + -1(7x + 9x2) = 0 5 + (7x * -1 + 9x2 * -1) = 0 5 + (-7x + -9x2) = 0 Solving 5 + -7x + -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'. -0.5555555556 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 0.7777777778x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 0.7777777778x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 0.7777777778x + x2 = 0 + 0.5555555556 0.7777777778x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 0.7777777778x + x2 = 0.5555555556 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 = 0.5555555556 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 0.5555555556 + 0.1512345679 Combine like terms: 0.5555555556 + 0.1512345679 = 0.7067901235 0.1512345679 + 0.7777777778x + x2 = 0.7067901235 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 0.7067901235 Calculate the square root of the right side: 0.840708108 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 0.840708108 and -0.840708108.Subproblem 1
x + 0.3888888889 = 0.840708108 Simplifying x + 0.3888888889 = 0.840708108 Reorder the terms: 0.3888888889 + x = 0.840708108 Solving 0.3888888889 + x = 0.840708108 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 = 0.840708108 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 0.840708108 + -0.3888888889 x = 0.840708108 + -0.3888888889 Combine like terms: 0.840708108 + -0.3888888889 = 0.4518192191 x = 0.4518192191 Simplifying x = 0.4518192191Subproblem 2
x + 0.3888888889 = -0.840708108 Simplifying x + 0.3888888889 = -0.840708108 Reorder the terms: 0.3888888889 + x = -0.840708108 Solving 0.3888888889 + x = -0.840708108 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 = -0.840708108 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -0.840708108 + -0.3888888889 x = -0.840708108 + -0.3888888889 Combine like terms: -0.840708108 + -0.3888888889 = -1.2295969969 x = -1.2295969969 Simplifying x = -1.2295969969Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4518192191, -1.2295969969}
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