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Simplifying 9x2 + -7x = 78 Reorder the terms: -7x + 9x2 = 78 Solving -7x + 9x2 = 78 Solving for variable 'x'. Reorder the terms: -78 + -7x + 9x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -78 + -7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -8.666666667 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '8.666666667' to each side of the equation. -8.666666667 + -0.7777777778x + 8.666666667 + x2 = 0 + 8.666666667 Reorder the terms: -8.666666667 + 8.666666667 + -0.7777777778x + x2 = 0 + 8.666666667 Combine like terms: -8.666666667 + 8.666666667 = 0.000000000 0.000000000 + -0.7777777778x + x2 = 0 + 8.666666667 -0.7777777778x + x2 = 0 + 8.666666667 Combine like terms: 0 + 8.666666667 = 8.666666667 -0.7777777778x + x2 = 8.666666667 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 = 8.666666667 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = 8.666666667 + 0.1512345679 Combine like terms: 8.666666667 + 0.1512345679 = 8.8179012349 0.1512345679 + -0.7777777778x + x2 = 8.8179012349 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 8.8179012349 Calculate the square root of the right side: 2.969495114 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 2.969495114 and -2.969495114.Subproblem 1
x + -0.3888888889 = 2.969495114 Simplifying x + -0.3888888889 = 2.969495114 Reorder the terms: -0.3888888889 + x = 2.969495114 Solving -0.3888888889 + x = 2.969495114 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 = 2.969495114 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 2.969495114 + 0.3888888889 x = 2.969495114 + 0.3888888889 Combine like terms: 2.969495114 + 0.3888888889 = 3.3583840029 x = 3.3583840029 Simplifying x = 3.3583840029Subproblem 2
x + -0.3888888889 = -2.969495114 Simplifying x + -0.3888888889 = -2.969495114 Reorder the terms: -0.3888888889 + x = -2.969495114 Solving -0.3888888889 + x = -2.969495114 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 = -2.969495114 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -2.969495114 + 0.3888888889 x = -2.969495114 + 0.3888888889 Combine like terms: -2.969495114 + 0.3888888889 = -2.5806062251 x = -2.5806062251 Simplifying x = -2.5806062251Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3583840029, -2.5806062251}
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