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Simplifying 3y + -8y2 + 4 = 0 Reorder the terms: 4 + 3y + -8y2 = 0 Solving 4 + 3y + -8y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.5 + -0.375y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.375y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.375y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.375y + y2 = 0 + 0.5 -0.375y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.375y + y2 = 0.5 The y term is -0.375y. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375y + 0.03515625 + y2 = 0.5 + 0.03515625 Reorder the terms: 0.03515625 + -0.375y + y2 = 0.5 + 0.03515625 Combine like terms: 0.5 + 0.03515625 = 0.53515625 0.03515625 + -0.375y + y2 = 0.53515625 Factor a perfect square on the left side: (y + -0.1875)(y + -0.1875) = 0.53515625 Calculate the square root of the right side: 0.731543744 Break this problem into two subproblems by setting (y + -0.1875) equal to 0.731543744 and -0.731543744.Subproblem 1
y + -0.1875 = 0.731543744 Simplifying y + -0.1875 = 0.731543744 Reorder the terms: -0.1875 + y = 0.731543744 Solving -0.1875 + y = 0.731543744 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + y = 0.731543744 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + y = 0.731543744 + 0.1875 y = 0.731543744 + 0.1875 Combine like terms: 0.731543744 + 0.1875 = 0.919043744 y = 0.919043744 Simplifying y = 0.919043744Subproblem 2
y + -0.1875 = -0.731543744 Simplifying y + -0.1875 = -0.731543744 Reorder the terms: -0.1875 + y = -0.731543744 Solving -0.1875 + y = -0.731543744 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + y = -0.731543744 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + y = -0.731543744 + 0.1875 y = -0.731543744 + 0.1875 Combine like terms: -0.731543744 + 0.1875 = -0.544043744 y = -0.544043744 Simplifying y = -0.544043744Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.919043744, -0.544043744}
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