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Simplifying 9x2 + -31x = 51 Reorder the terms: -31x + 9x2 = 51 Solving -31x + 9x2 = 51 Solving for variable 'x'. Reorder the terms: -51 + -31x + 9x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + -31x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.666666667 + -3.444444444x + x2 = 0 Move the constant term to the right: Add '5.666666667' to each side of the equation. -5.666666667 + -3.444444444x + 5.666666667 + x2 = 0 + 5.666666667 Reorder the terms: -5.666666667 + 5.666666667 + -3.444444444x + x2 = 0 + 5.666666667 Combine like terms: -5.666666667 + 5.666666667 = 0.000000000 0.000000000 + -3.444444444x + x2 = 0 + 5.666666667 -3.444444444x + x2 = 0 + 5.666666667 Combine like terms: 0 + 5.666666667 = 5.666666667 -3.444444444x + x2 = 5.666666667 The x term is -3.444444444x. Take half its coefficient (-1.722222222). Square it (2.966049382) and add it to both sides. Add '2.966049382' to each side of the equation. -3.444444444x + 2.966049382 + x2 = 5.666666667 + 2.966049382 Reorder the terms: 2.966049382 + -3.444444444x + x2 = 5.666666667 + 2.966049382 Combine like terms: 5.666666667 + 2.966049382 = 8.632716049 2.966049382 + -3.444444444x + x2 = 8.632716049 Factor a perfect square on the left side: (x + -1.722222222)(x + -1.722222222) = 8.632716049 Calculate the square root of the right side: 2.938148405 Break this problem into two subproblems by setting (x + -1.722222222) equal to 2.938148405 and -2.938148405.Subproblem 1
x + -1.722222222 = 2.938148405 Simplifying x + -1.722222222 = 2.938148405 Reorder the terms: -1.722222222 + x = 2.938148405 Solving -1.722222222 + x = 2.938148405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.722222222' to each side of the equation. -1.722222222 + 1.722222222 + x = 2.938148405 + 1.722222222 Combine like terms: -1.722222222 + 1.722222222 = 0.000000000 0.000000000 + x = 2.938148405 + 1.722222222 x = 2.938148405 + 1.722222222 Combine like terms: 2.938148405 + 1.722222222 = 4.660370627 x = 4.660370627 Simplifying x = 4.660370627Subproblem 2
x + -1.722222222 = -2.938148405 Simplifying x + -1.722222222 = -2.938148405 Reorder the terms: -1.722222222 + x = -2.938148405 Solving -1.722222222 + x = -2.938148405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.722222222' to each side of the equation. -1.722222222 + 1.722222222 + x = -2.938148405 + 1.722222222 Combine like terms: -1.722222222 + 1.722222222 = 0.000000000 0.000000000 + x = -2.938148405 + 1.722222222 x = -2.938148405 + 1.722222222 Combine like terms: -2.938148405 + 1.722222222 = -1.215926183 x = -1.215926183 Simplifying x = -1.215926183Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.660370627, -1.215926183}
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