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Simplifying x2 + -8x + 4.55 = 0 Reorder the terms: 4.55 + -8x + x2 = 0 Solving 4.55 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4.55' to each side of the equation. 4.55 + -8x + -4.55 + x2 = 0 + -4.55 Reorder the terms: 4.55 + -4.55 + -8x + x2 = 0 + -4.55 Combine like terms: 4.55 + -4.55 = 0.00 0.00 + -8x + x2 = 0 + -4.55 -8x + x2 = 0 + -4.55 Combine like terms: 0 + -4.55 = -4.55 -8x + x2 = -4.55 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -4.55 + 16 Reorder the terms: 16 + -8x + x2 = -4.55 + 16 Combine like terms: -4.55 + 16 = 11.45 16 + -8x + x2 = 11.45 Factor a perfect square on the left side: (x + -4)(x + -4) = 11.45 Calculate the square root of the right side: 3.383784863 Break this problem into two subproblems by setting (x + -4) equal to 3.383784863 and -3.383784863.Subproblem 1
x + -4 = 3.383784863 Simplifying x + -4 = 3.383784863 Reorder the terms: -4 + x = 3.383784863 Solving -4 + x = 3.383784863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.383784863 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.383784863 + 4 x = 3.383784863 + 4 Combine like terms: 3.383784863 + 4 = 7.383784863 x = 7.383784863 Simplifying x = 7.383784863Subproblem 2
x + -4 = -3.383784863 Simplifying x + -4 = -3.383784863 Reorder the terms: -4 + x = -3.383784863 Solving -4 + x = -3.383784863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.383784863 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.383784863 + 4 x = -3.383784863 + 4 Combine like terms: -3.383784863 + 4 = 0.616215137 x = 0.616215137 Simplifying x = 0.616215137Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.383784863, 0.616215137}
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