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Simplifying 4x2 + 0.25x + -1.125 = 0 Reorder the terms: -1.125 + 0.25x + 4x2 = 0 Solving -1.125 + 0.25x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.28125 + 0.0625x + x2 = 0 Move the constant term to the right: Add '0.28125' to each side of the equation. -0.28125 + 0.0625x + 0.28125 + x2 = 0 + 0.28125 Reorder the terms: -0.28125 + 0.28125 + 0.0625x + x2 = 0 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + 0.0625x + x2 = 0 + 0.28125 0.0625x + x2 = 0 + 0.28125 Combine like terms: 0 + 0.28125 = 0.28125 0.0625x + x2 = 0.28125 The x term is 0.0625x. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625x + 0.0009765625 + x2 = 0.28125 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625x + x2 = 0.28125 + 0.0009765625 Combine like terms: 0.28125 + 0.0009765625 = 0.2822265625 0.0009765625 + 0.0625x + x2 = 0.2822265625 Factor a perfect square on the left side: (x + 0.03125)(x + 0.03125) = 0.2822265625 Calculate the square root of the right side: 0.53125 Break this problem into two subproblems by setting (x + 0.03125) equal to 0.53125 and -0.53125.Subproblem 1
x + 0.03125 = 0.53125 Simplifying x + 0.03125 = 0.53125 Reorder the terms: 0.03125 + x = 0.53125 Solving 0.03125 + x = 0.53125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = 0.53125 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = 0.53125 + -0.03125 x = 0.53125 + -0.03125 Combine like terms: 0.53125 + -0.03125 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 0.03125 = -0.53125 Simplifying x + 0.03125 = -0.53125 Reorder the terms: 0.03125 + x = -0.53125 Solving 0.03125 + x = -0.53125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = -0.53125 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = -0.53125 + -0.03125 x = -0.53125 + -0.03125 Combine like terms: -0.53125 + -0.03125 = -0.5625 x = -0.5625 Simplifying x = -0.5625Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -0.5625}
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