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Simplifying -16x2 + -2.5x + 3 = 0 Reorder the terms: 3 + -2.5x + -16x2 = 0 Solving 3 + -2.5x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.1875 + 0.15625x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 0.15625x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 0.15625x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 0.15625x + x2 = 0 + 0.1875 0.15625x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 0.15625x + x2 = 0.1875 The x term is 0.15625x. Take half its coefficient (0.078125). Square it (0.006103515625) and add it to both sides. Add '0.006103515625' to each side of the equation. 0.15625x + 0.006103515625 + x2 = 0.1875 + 0.006103515625 Reorder the terms: 0.006103515625 + 0.15625x + x2 = 0.1875 + 0.006103515625 Combine like terms: 0.1875 + 0.006103515625 = 0.193603515625 0.006103515625 + 0.15625x + x2 = 0.193603515625 Factor a perfect square on the left side: (x + 0.078125)(x + 0.078125) = 0.193603515625 Calculate the square root of the right side: 0.440003995 Break this problem into two subproblems by setting (x + 0.078125) equal to 0.440003995 and -0.440003995.Subproblem 1
x + 0.078125 = 0.440003995 Simplifying x + 0.078125 = 0.440003995 Reorder the terms: 0.078125 + x = 0.440003995 Solving 0.078125 + x = 0.440003995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.078125' to each side of the equation. 0.078125 + -0.078125 + x = 0.440003995 + -0.078125 Combine like terms: 0.078125 + -0.078125 = 0.000000 0.000000 + x = 0.440003995 + -0.078125 x = 0.440003995 + -0.078125 Combine like terms: 0.440003995 + -0.078125 = 0.361878995 x = 0.361878995 Simplifying x = 0.361878995Subproblem 2
x + 0.078125 = -0.440003995 Simplifying x + 0.078125 = -0.440003995 Reorder the terms: 0.078125 + x = -0.440003995 Solving 0.078125 + x = -0.440003995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.078125' to each side of the equation. 0.078125 + -0.078125 + x = -0.440003995 + -0.078125 Combine like terms: 0.078125 + -0.078125 = 0.000000 0.000000 + x = -0.440003995 + -0.078125 x = -0.440003995 + -0.078125 Combine like terms: -0.440003995 + -0.078125 = -0.518128995 x = -0.518128995 Simplifying x = -0.518128995Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.361878995, -0.518128995}
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