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Simplifying x2 + -0.25x + -0.55 = 0 Reorder the terms: -0.55 + -0.25x + x2 = 0 Solving -0.55 + -0.25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.55' to each side of the equation. -0.55 + -0.25x + 0.55 + x2 = 0 + 0.55 Reorder the terms: -0.55 + 0.55 + -0.25x + x2 = 0 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + -0.25x + x2 = 0 + 0.55 -0.25x + x2 = 0 + 0.55 Combine like terms: 0 + 0.55 = 0.55 -0.25x + x2 = 0.55 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.55 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.55 + 0.015625 Combine like terms: 0.55 + 0.015625 = 0.565625 0.015625 + -0.25x + x2 = 0.565625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.565625 Calculate the square root of the right side: 0.752080448 Break this problem into two subproblems by setting (x + -0.125) equal to 0.752080448 and -0.752080448.Subproblem 1
x + -0.125 = 0.752080448 Simplifying x + -0.125 = 0.752080448 Reorder the terms: -0.125 + x = 0.752080448 Solving -0.125 + x = 0.752080448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.752080448 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.752080448 + 0.125 x = 0.752080448 + 0.125 Combine like terms: 0.752080448 + 0.125 = 0.877080448 x = 0.877080448 Simplifying x = 0.877080448Subproblem 2
x + -0.125 = -0.752080448 Simplifying x + -0.125 = -0.752080448 Reorder the terms: -0.125 + x = -0.752080448 Solving -0.125 + x = -0.752080448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.752080448 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.752080448 + 0.125 x = -0.752080448 + 0.125 Combine like terms: -0.752080448 + 0.125 = -0.627080448 x = -0.627080448 Simplifying x = -0.627080448Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.877080448, -0.627080448}
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