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Simplifying 3x2 + 1.5x = 220 Reorder the terms: 1.5x + 3x2 = 220 Solving 1.5x + 3x2 = 220 Solving for variable 'x'. Reorder the terms: -220 + 1.5x + 3x2 = 220 + -220 Combine like terms: 220 + -220 = 0 -220 + 1.5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -73.33333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '73.33333333' to each side of the equation. -73.33333333 + 0.5x + 73.33333333 + x2 = 0 + 73.33333333 Reorder the terms: -73.33333333 + 73.33333333 + 0.5x + x2 = 0 + 73.33333333 Combine like terms: -73.33333333 + 73.33333333 = 0.00000000 0.00000000 + 0.5x + x2 = 0 + 73.33333333 0.5x + x2 = 0 + 73.33333333 Combine like terms: 0 + 73.33333333 = 73.33333333 0.5x + x2 = 73.33333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 73.33333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 73.33333333 + 0.0625 Combine like terms: 73.33333333 + 0.0625 = 73.39583333 0.0625 + 0.5x + x2 = 73.39583333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 73.39583333 Calculate the square root of the right side: 8.567136822 Break this problem into two subproblems by setting (x + 0.25) equal to 8.567136822 and -8.567136822.Subproblem 1
x + 0.25 = 8.567136822 Simplifying x + 0.25 = 8.567136822 Reorder the terms: 0.25 + x = 8.567136822 Solving 0.25 + x = 8.567136822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 8.567136822 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 8.567136822 + -0.25 x = 8.567136822 + -0.25 Combine like terms: 8.567136822 + -0.25 = 8.317136822 x = 8.317136822 Simplifying x = 8.317136822Subproblem 2
x + 0.25 = -8.567136822 Simplifying x + 0.25 = -8.567136822 Reorder the terms: 0.25 + x = -8.567136822 Solving 0.25 + x = -8.567136822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -8.567136822 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -8.567136822 + -0.25 x = -8.567136822 + -0.25 Combine like terms: -8.567136822 + -0.25 = -8.817136822 x = -8.817136822 Simplifying x = -8.817136822Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.317136822, -8.817136822}
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