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Simplifying 9x2 + 22x + 3 = 0 Reorder the terms: 3 + 22x + 9x2 = 0 Solving 3 + 22x + 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'. 0.3333333333 + 2.444444444x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 2.444444444x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 2.444444444x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 2.444444444x + x2 = 0 + -0.3333333333 2.444444444x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 2.444444444x + x2 = -0.3333333333 The x term is 2.444444444x. Take half its coefficient (1.222222222). Square it (1.493827160) and add it to both sides. Add '1.493827160' to each side of the equation. 2.444444444x + 1.493827160 + x2 = -0.3333333333 + 1.493827160 Reorder the terms: 1.493827160 + 2.444444444x + x2 = -0.3333333333 + 1.493827160 Combine like terms: -0.3333333333 + 1.493827160 = 1.1604938267 1.493827160 + 2.444444444x + x2 = 1.1604938267 Factor a perfect square on the left side: (x + 1.222222222)(x + 1.222222222) = 1.1604938267 Calculate the square root of the right side: 1.07726219 Break this problem into two subproblems by setting (x + 1.222222222) equal to 1.07726219 and -1.07726219.Subproblem 1
x + 1.222222222 = 1.07726219 Simplifying x + 1.222222222 = 1.07726219 Reorder the terms: 1.222222222 + x = 1.07726219 Solving 1.222222222 + x = 1.07726219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.222222222' to each side of the equation. 1.222222222 + -1.222222222 + x = 1.07726219 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + x = 1.07726219 + -1.222222222 x = 1.07726219 + -1.222222222 Combine like terms: 1.07726219 + -1.222222222 = -0.144960032 x = -0.144960032 Simplifying x = -0.144960032Subproblem 2
x + 1.222222222 = -1.07726219 Simplifying x + 1.222222222 = -1.07726219 Reorder the terms: 1.222222222 + x = -1.07726219 Solving 1.222222222 + x = -1.07726219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.222222222' to each side of the equation. 1.222222222 + -1.222222222 + x = -1.07726219 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + x = -1.07726219 + -1.222222222 x = -1.07726219 + -1.222222222 Combine like terms: -1.07726219 + -1.222222222 = -2.299484412 x = -2.299484412 Simplifying x = -2.299484412Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.144960032, -2.299484412}
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