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Simplifying 9x2 + -70x + 40 = 0 Reorder the terms: 40 + -70x + 9x2 = 0 Solving 40 + -70x + 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'. 4.444444444 + -7.777777778x + x2 = 0 Move the constant term to the right: Add '-4.444444444' to each side of the equation. 4.444444444 + -7.777777778x + -4.444444444 + x2 = 0 + -4.444444444 Reorder the terms: 4.444444444 + -4.444444444 + -7.777777778x + x2 = 0 + -4.444444444 Combine like terms: 4.444444444 + -4.444444444 = 0.000000000 0.000000000 + -7.777777778x + x2 = 0 + -4.444444444 -7.777777778x + x2 = 0 + -4.444444444 Combine like terms: 0 + -4.444444444 = -4.444444444 -7.777777778x + x2 = -4.444444444 The x term is -7.777777778x. Take half its coefficient (-3.888888889). Square it (15.12345679) and add it to both sides. Add '15.12345679' to each side of the equation. -7.777777778x + 15.12345679 + x2 = -4.444444444 + 15.12345679 Reorder the terms: 15.12345679 + -7.777777778x + x2 = -4.444444444 + 15.12345679 Combine like terms: -4.444444444 + 15.12345679 = 10.679012346 15.12345679 + -7.777777778x + x2 = 10.679012346 Factor a perfect square on the left side: (x + -3.888888889)(x + -3.888888889) = 10.679012346 Calculate the square root of the right side: 3.267875816 Break this problem into two subproblems by setting (x + -3.888888889) equal to 3.267875816 and -3.267875816.Subproblem 1
x + -3.888888889 = 3.267875816 Simplifying x + -3.888888889 = 3.267875816 Reorder the terms: -3.888888889 + x = 3.267875816 Solving -3.888888889 + x = 3.267875816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.888888889' to each side of the equation. -3.888888889 + 3.888888889 + x = 3.267875816 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + x = 3.267875816 + 3.888888889 x = 3.267875816 + 3.888888889 Combine like terms: 3.267875816 + 3.888888889 = 7.156764705 x = 7.156764705 Simplifying x = 7.156764705Subproblem 2
x + -3.888888889 = -3.267875816 Simplifying x + -3.888888889 = -3.267875816 Reorder the terms: -3.888888889 + x = -3.267875816 Solving -3.888888889 + x = -3.267875816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.888888889' to each side of the equation. -3.888888889 + 3.888888889 + x = -3.267875816 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + x = -3.267875816 + 3.888888889 x = -3.267875816 + 3.888888889 Combine like terms: -3.267875816 + 3.888888889 = 0.621013073 x = 0.621013073 Simplifying x = 0.621013073Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.156764705, 0.621013073}
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