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Simplifying x2 + -3x + 4 = 50 Reorder the terms: 4 + -3x + x2 = 50 Solving 4 + -3x + x2 = 50 Solving for variable 'x'. Reorder the terms: 4 + -50 + -3x + x2 = 50 + -50 Combine like terms: 4 + -50 = -46 -46 + -3x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -46 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -3x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + -3x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -3x + x2 = 0 + 46 -3x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 -3x + x2 = 46 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 = 46 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 46 + 2.25 Combine like terms: 46 + 2.25 = 48.25 2.25 + -3x + x2 = 48.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + -1.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + -1.5 = 6.946221995 Simplifying x + -1.5 = 6.946221995 Reorder the terms: -1.5 + x = 6.946221995 Solving -1.5 + x = 6.946221995 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 = 6.946221995 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.946221995 + 1.5 x = 6.946221995 + 1.5 Combine like terms: 6.946221995 + 1.5 = 8.446221995 x = 8.446221995 Simplifying x = 8.446221995Subproblem 2
x + -1.5 = -6.946221995 Simplifying x + -1.5 = -6.946221995 Reorder the terms: -1.5 + x = -6.946221995 Solving -1.5 + x = -6.946221995 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 = -6.946221995 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.946221995 + 1.5 x = -6.946221995 + 1.5 Combine like terms: -6.946221995 + 1.5 = -5.446221995 x = -5.446221995 Simplifying x = -5.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.446221995, -5.446221995}
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