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Simplifying (3x * 3x) + 22x + 4 = -3 Reorder the terms for easier multiplication: (3 * 3x * x) + 22x + 4 = -3 Multiply 3 * 3 (9x * x) + 22x + 4 = -3 Multiply x * x (9x2) + 22x + 4 = -3 Reorder the terms: 4 + 22x + (9x2) = -3 Solving 4 + 22x + (9x2) = -3 Solving for variable 'x'. Reorder the terms: 4 + 3 + 22x + (9x2) = -3 + 3 Combine like terms: 4 + 3 = 7 7 + 22x + (9x2) = -3 + 3 Combine like terms: -3 + 3 = 0 7 + 22x + (9x2) = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + 2.444444444x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + 2.444444444x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + 2.444444444x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + 2.444444444x + x2 = 0 + -0.7777777778 2.444444444x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 2.444444444x + x2 = -0.7777777778 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 = -0.7777777778 + 1.493827160 Reorder the terms: 1.493827160 + 2.444444444x + x2 = -0.7777777778 + 1.493827160 Combine like terms: -0.7777777778 + 1.493827160 = 0.7160493822 1.493827160 + 2.444444444x + x2 = 0.7160493822 Factor a perfect square on the left side: ((x) + 1.222222222)((x) + 1.222222222) = 0.7160493822 Calculate the square root of the right side: 0.846197011 Break this problem into two subproblems by setting ((x) + 1.222222222) equal to 0.846197011 and -0.846197011.Subproblem 1
(x) + 1.222222222 = 0.846197011 Simplifying (x) + 1.222222222 = 0.846197011 x + 1.222222222 = 0.846197011 Reorder the terms: 1.222222222 + x = 0.846197011 Solving 1.222222222 + x = 0.846197011 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 = 0.846197011 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + x = 0.846197011 + -1.222222222 x = 0.846197011 + -1.222222222 Combine like terms: 0.846197011 + -1.222222222 = -0.376025211 x = -0.376025211 Simplifying x = -0.376025211Subproblem 2
(x) + 1.222222222 = -0.846197011 Simplifying (x) + 1.222222222 = -0.846197011 x + 1.222222222 = -0.846197011 Reorder the terms: 1.222222222 + x = -0.846197011 Solving 1.222222222 + x = -0.846197011 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 = -0.846197011 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + x = -0.846197011 + -1.222222222 x = -0.846197011 + -1.222222222 Combine like terms: -0.846197011 + -1.222222222 = -2.068419233 x = -2.068419233 Simplifying x = -2.068419233Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.376025211, -2.068419233}
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