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Simplifying x2 + -3x = x + 3.8 Reorder the terms: -3x + x2 = x + 3.8 Reorder the terms: -3x + x2 = 3.8 + x Solving -3x + x2 = 3.8 + x Solving for variable 'x'. Reorder the terms: -3.8 + -3x + -1x + x2 = 3.8 + x + -3.8 + -1x Combine like terms: -3x + -1x = -4x -3.8 + -4x + x2 = 3.8 + x + -3.8 + -1x Reorder the terms: -3.8 + -4x + x2 = 3.8 + -3.8 + x + -1x Combine like terms: 3.8 + -3.8 = 0.0 -3.8 + -4x + x2 = 0.0 + x + -1x -3.8 + -4x + x2 = x + -1x Combine like terms: x + -1x = 0 -3.8 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + -4x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + -4x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + -4x + x2 = 0 + 3.8 -4x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 -4x + x2 = 3.8 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 3.8 + 4 Reorder the terms: 4 + -4x + x2 = 3.8 + 4 Combine like terms: 3.8 + 4 = 7.8 4 + -4x + x2 = 7.8 Factor a perfect square on the left side: (x + -2)(x + -2) = 7.8 Calculate the square root of the right side: 2.792848009 Break this problem into two subproblems by setting (x + -2) equal to 2.792848009 and -2.792848009.Subproblem 1
x + -2 = 2.792848009 Simplifying x + -2 = 2.792848009 Reorder the terms: -2 + x = 2.792848009 Solving -2 + x = 2.792848009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.792848009 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.792848009 + 2 x = 2.792848009 + 2 Combine like terms: 2.792848009 + 2 = 4.792848009 x = 4.792848009 Simplifying x = 4.792848009Subproblem 2
x + -2 = -2.792848009 Simplifying x + -2 = -2.792848009 Reorder the terms: -2 + x = -2.792848009 Solving -2 + x = -2.792848009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.792848009 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.792848009 + 2 x = -2.792848009 + 2 Combine like terms: -2.792848009 + 2 = -0.792848009 x = -0.792848009 Simplifying x = -0.792848009Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.792848009, -0.792848009}
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