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Simplifying 0.2(x + 30) * 0.6x = 22 Reorder the terms: 0.2(30 + x) * 0.6x = 22 Reorder the terms for easier multiplication: 0.2 * 0.6x(30 + x) = 22 Multiply 0.2 * 0.6 0.12x(30 + x) = 22 (30 * 0.12x + x * 0.12x) = 22 (3.6x + 0.12x2) = 22 Solving 3.6x + 0.12x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + 3.6x + 0.12x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 3.6x + 0.12x2 = 0 Begin completing the square. Divide all terms by 0.12 the coefficient of the squared term: Divide each side by '0.12'. -183.3333333 + 30x + x2 = 0 Move the constant term to the right: Add '183.3333333' to each side of the equation. -183.3333333 + 30x + 183.3333333 + x2 = 0 + 183.3333333 Reorder the terms: -183.3333333 + 183.3333333 + 30x + x2 = 0 + 183.3333333 Combine like terms: -183.3333333 + 183.3333333 = 0.0000000 0.0000000 + 30x + x2 = 0 + 183.3333333 30x + x2 = 0 + 183.3333333 Combine like terms: 0 + 183.3333333 = 183.3333333 30x + x2 = 183.3333333 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 183.3333333 + 225 Reorder the terms: 225 + 30x + x2 = 183.3333333 + 225 Combine like terms: 183.3333333 + 225 = 408.3333333 225 + 30x + x2 = 408.3333333 Factor a perfect square on the left side: (x + 15)(x + 15) = 408.3333333 Calculate the square root of the right side: 20.207259421 Break this problem into two subproblems by setting (x + 15) equal to 20.207259421 and -20.207259421.Subproblem 1
x + 15 = 20.207259421 Simplifying x + 15 = 20.207259421 Reorder the terms: 15 + x = 20.207259421 Solving 15 + x = 20.207259421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 20.207259421 + -15 Combine like terms: 15 + -15 = 0 0 + x = 20.207259421 + -15 x = 20.207259421 + -15 Combine like terms: 20.207259421 + -15 = 5.207259421 x = 5.207259421 Simplifying x = 5.207259421Subproblem 2
x + 15 = -20.207259421 Simplifying x + 15 = -20.207259421 Reorder the terms: 15 + x = -20.207259421 Solving 15 + x = -20.207259421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -20.207259421 + -15 Combine like terms: 15 + -15 = 0 0 + x = -20.207259421 + -15 x = -20.207259421 + -15 Combine like terms: -20.207259421 + -15 = -35.207259421 x = -35.207259421 Simplifying x = -35.207259421Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.207259421, -35.207259421}
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