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Simplifying 9x2 + 30x + 25 = 18 Reorder the terms: 25 + 30x + 9x2 = 18 Solving 25 + 30x + 9x2 = 18 Solving for variable 'x'. Reorder the terms: 25 + -18 + 30x + 9x2 = 18 + -18 Combine like terms: 25 + -18 = 7 7 + 30x + 9x2 = 18 + -18 Combine like terms: 18 + -18 = 0 7 + 30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + 3.333333333x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + 3.333333333x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + 3.333333333x + x2 = 0 + -0.7777777778 3.333333333x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 3.333333333x + x2 = -0.7777777778 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 = -0.7777777778 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = -0.7777777778 + 2.777777779 Combine like terms: -0.7777777778 + 2.777777779 = 2.0000000012 2.777777779 + 3.333333333x + x2 = 2.0000000012 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 2.0000000012 Calculate the square root of the right side: 1.414213563 Break this problem into two subproblems by setting (x + 1.666666667) equal to 1.414213563 and -1.414213563.Subproblem 1
x + 1.666666667 = 1.414213563 Simplifying x + 1.666666667 = 1.414213563 Reorder the terms: 1.666666667 + x = 1.414213563 Solving 1.666666667 + x = 1.414213563 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 = 1.414213563 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 1.414213563 + -1.666666667 x = 1.414213563 + -1.666666667 Combine like terms: 1.414213563 + -1.666666667 = -0.252453104 x = -0.252453104 Simplifying x = -0.252453104Subproblem 2
x + 1.666666667 = -1.414213563 Simplifying x + 1.666666667 = -1.414213563 Reorder the terms: 1.666666667 + x = -1.414213563 Solving 1.666666667 + x = -1.414213563 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 = -1.414213563 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -1.414213563 + -1.666666667 x = -1.414213563 + -1.666666667 Combine like terms: -1.414213563 + -1.666666667 = -3.08088023 x = -3.08088023 Simplifying x = -3.08088023Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.252453104, -3.08088023}
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