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Simplifying 9x2 + -49x + -30 = 30 Reorder the terms: -30 + -49x + 9x2 = 30 Solving -30 + -49x + 9x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + -30 + -49x + 9x2 = 30 + -30 Combine like terms: -30 + -30 = -60 -60 + -49x + 9x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -60 + -49x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.666666667 + -5.444444444x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -5.444444444x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -5.444444444x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -5.444444444x + x2 = 0 + 6.666666667 -5.444444444x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -5.444444444x + x2 = 6.666666667 The x term is -5.444444444x. Take half its coefficient (-2.722222222). Square it (7.410493826) and add it to both sides. Add '7.410493826' to each side of the equation. -5.444444444x + 7.410493826 + x2 = 6.666666667 + 7.410493826 Reorder the terms: 7.410493826 + -5.444444444x + x2 = 6.666666667 + 7.410493826 Combine like terms: 6.666666667 + 7.410493826 = 14.077160493 7.410493826 + -5.444444444x + x2 = 14.077160493 Factor a perfect square on the left side: (x + -2.722222222)(x + -2.722222222) = 14.077160493 Calculate the square root of the right side: 3.751954223 Break this problem into two subproblems by setting (x + -2.722222222) equal to 3.751954223 and -3.751954223.Subproblem 1
x + -2.722222222 = 3.751954223 Simplifying x + -2.722222222 = 3.751954223 Reorder the terms: -2.722222222 + x = 3.751954223 Solving -2.722222222 + x = 3.751954223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.722222222' to each side of the equation. -2.722222222 + 2.722222222 + x = 3.751954223 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + x = 3.751954223 + 2.722222222 x = 3.751954223 + 2.722222222 Combine like terms: 3.751954223 + 2.722222222 = 6.474176445 x = 6.474176445 Simplifying x = 6.474176445Subproblem 2
x + -2.722222222 = -3.751954223 Simplifying x + -2.722222222 = -3.751954223 Reorder the terms: -2.722222222 + x = -3.751954223 Solving -2.722222222 + x = -3.751954223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.722222222' to each side of the equation. -2.722222222 + 2.722222222 + x = -3.751954223 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + x = -3.751954223 + 2.722222222 x = -3.751954223 + 2.722222222 Combine like terms: -3.751954223 + 2.722222222 = -1.029732001 x = -1.029732001 Simplifying x = -1.029732001Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.474176445, -1.029732001}
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