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Simplifying x2 + -3x + 1 = 48 Reorder the terms: 1 + -3x + x2 = 48 Solving 1 + -3x + x2 = 48 Solving for variable 'x'. Reorder the terms: 1 + -48 + -3x + x2 = 48 + -48 Combine like terms: 1 + -48 = -47 -47 + -3x + x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -47 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -3x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + -3x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -3x + x2 = 0 + 47 -3x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 -3x + x2 = 47 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 47 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 47 + 2.25 Combine like terms: 47 + 2.25 = 49.25 2.25 + -3x + x2 = 49.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + -1.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + -1.5 = 7.017834424 Simplifying x + -1.5 = 7.017834424 Reorder the terms: -1.5 + x = 7.017834424 Solving -1.5 + x = 7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 7.017834424 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 7.017834424 + 1.5 x = 7.017834424 + 1.5 Combine like terms: 7.017834424 + 1.5 = 8.517834424 x = 8.517834424 Simplifying x = 8.517834424Subproblem 2
x + -1.5 = -7.017834424 Simplifying x + -1.5 = -7.017834424 Reorder the terms: -1.5 + x = -7.017834424 Solving -1.5 + x = -7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -7.017834424 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -7.017834424 + 1.5 x = -7.017834424 + 1.5 Combine like terms: -7.017834424 + 1.5 = -5.517834424 x = -5.517834424 Simplifying x = -5.517834424Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.517834424, -5.517834424}
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