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Simplifying 9x2 + 18x + 7 = 0 Reorder the terms: 7 + 18x + 9x2 = 0 Solving 7 + 18x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + 2x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + 2x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + 2x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.7777777778 2x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 2x + x2 = -0.7777777778 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.7777777778 + 1 Reorder the terms: 1 + 2x + x2 = -0.7777777778 + 1 Combine like terms: -0.7777777778 + 1 = 0.2222222222 1 + 2x + x2 = 0.2222222222 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.2222222222 Calculate the square root of the right side: 0.471404521 Break this problem into two subproblems by setting (x + 1) equal to 0.471404521 and -0.471404521.Subproblem 1
x + 1 = 0.471404521 Simplifying x + 1 = 0.471404521 Reorder the terms: 1 + x = 0.471404521 Solving 1 + x = 0.471404521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.471404521 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.471404521 + -1 x = 0.471404521 + -1 Combine like terms: 0.471404521 + -1 = -0.528595479 x = -0.528595479 Simplifying x = -0.528595479Subproblem 2
x + 1 = -0.471404521 Simplifying x + 1 = -0.471404521 Reorder the terms: 1 + x = -0.471404521 Solving 1 + x = -0.471404521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.471404521 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.471404521 + -1 x = -0.471404521 + -1 Combine like terms: -0.471404521 + -1 = -1.471404521 x = -1.471404521 Simplifying x = -1.471404521Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.528595479, -1.471404521}
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