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Simplifying 9x2 + 15x + 2 = 0 Reorder the terms: 2 + 15x + 9x2 = 0 Solving 2 + 15x + 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'. 0.2222222222 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 1.666666667x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 1.666666667x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 1.666666667x + x2 = 0 + -0.2222222222 1.666666667x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 1.666666667x + x2 = -0.2222222222 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = -0.2222222222 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = -0.2222222222 + 0.6944444447 Combine like terms: -0.2222222222 + 0.6944444447 = 0.4722222225 0.6944444447 + 1.666666667x + x2 = 0.4722222225 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 0.4722222225 Calculate the square root of the right side: 0.687184271 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 0.687184271 and -0.687184271.Subproblem 1
x + 0.8333333335 = 0.687184271 Simplifying x + 0.8333333335 = 0.687184271 Reorder the terms: 0.8333333335 + x = 0.687184271 Solving 0.8333333335 + x = 0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 0.687184271 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 0.687184271 + -0.8333333335 x = 0.687184271 + -0.8333333335 Combine like terms: 0.687184271 + -0.8333333335 = -0.1461490625 x = -0.1461490625 Simplifying x = -0.1461490625Subproblem 2
x + 0.8333333335 = -0.687184271 Simplifying x + 0.8333333335 = -0.687184271 Reorder the terms: 0.8333333335 + x = -0.687184271 Solving 0.8333333335 + x = -0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -0.687184271 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -0.687184271 + -0.8333333335 x = -0.687184271 + -0.8333333335 Combine like terms: -0.687184271 + -0.8333333335 = -1.5205176045 x = -1.5205176045 Simplifying x = -1.5205176045Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1461490625, -1.5205176045}
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