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Simplifying 4x2 + 5x + 1.25 = 0 Reorder the terms: 1.25 + 5x + 4x2 = 0 Solving 1.25 + 5x + 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'. 0.3125 + 1.25x + x2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + 1.25x + -0.3125 + x2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + 1.25x + x2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + 1.25x + x2 = 0 + -0.3125 1.25x + x2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 1.25x + x2 = -0.3125 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -0.3125 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -0.3125 + 0.390625 Combine like terms: -0.3125 + 0.390625 = 0.078125 0.390625 + 1.25x + x2 = 0.078125 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 0.078125 Calculate the square root of the right side: 0.279508497 Break this problem into two subproblems by setting (x + 0.625) equal to 0.279508497 and -0.279508497.Subproblem 1
x + 0.625 = 0.279508497 Simplifying x + 0.625 = 0.279508497 Reorder the terms: 0.625 + x = 0.279508497 Solving 0.625 + x = 0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 0.279508497 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 0.279508497 + -0.625 x = 0.279508497 + -0.625 Combine like terms: 0.279508497 + -0.625 = -0.345491503 x = -0.345491503 Simplifying x = -0.345491503Subproblem 2
x + 0.625 = -0.279508497 Simplifying x + 0.625 = -0.279508497 Reorder the terms: 0.625 + x = -0.279508497 Solving 0.625 + x = -0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -0.279508497 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -0.279508497 + -0.625 x = -0.279508497 + -0.625 Combine like terms: -0.279508497 + -0.625 = -0.904508497 x = -0.904508497 Simplifying x = -0.904508497Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.345491503, -0.904508497}
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