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Simplifying 9x2 + 30x + 25 = 72 Reorder the terms: 25 + 30x + 9x2 = 72 Solving 25 + 30x + 9x2 = 72 Solving for variable 'x'. Reorder the terms: 25 + -72 + 30x + 9x2 = 72 + -72 Combine like terms: 25 + -72 = -47 -47 + 30x + 9x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -47 + 30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.222222222 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '5.222222222' to each side of the equation. -5.222222222 + 3.333333333x + 5.222222222 + x2 = 0 + 5.222222222 Reorder the terms: -5.222222222 + 5.222222222 + 3.333333333x + x2 = 0 + 5.222222222 Combine like terms: -5.222222222 + 5.222222222 = 0.000000000 0.000000000 + 3.333333333x + x2 = 0 + 5.222222222 3.333333333x + x2 = 0 + 5.222222222 Combine like terms: 0 + 5.222222222 = 5.222222222 3.333333333x + x2 = 5.222222222 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 5.222222222 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 5.222222222 + 2.777777779 Combine like terms: 5.222222222 + 2.777777779 = 8.000000001 2.777777779 + 3.333333333x + x2 = 8.000000001 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 8.000000001 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + 1.666666667) equal to 2.828427125 and -2.828427125.Subproblem 1
x + 1.666666667 = 2.828427125 Simplifying x + 1.666666667 = 2.828427125 Reorder the terms: 1.666666667 + x = 2.828427125 Solving 1.666666667 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 2.828427125 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 2.828427125 + -1.666666667 x = 2.828427125 + -1.666666667 Combine like terms: 2.828427125 + -1.666666667 = 1.161760458 x = 1.161760458 Simplifying x = 1.161760458Subproblem 2
x + 1.666666667 = -2.828427125 Simplifying x + 1.666666667 = -2.828427125 Reorder the terms: 1.666666667 + x = -2.828427125 Solving 1.666666667 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -2.828427125 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -2.828427125 + -1.666666667 x = -2.828427125 + -1.666666667 Combine like terms: -2.828427125 + -1.666666667 = -4.495093792 x = -4.495093792 Simplifying x = -4.495093792Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.161760458, -4.495093792}
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