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Simplifying 4y2 + -0.76 * 2.0 + -2y = 0 Multiply -0.76 * 2.0 4y2 + -1.52 + -2y = 0 Reorder the terms: -1.52 + -2y + 4y2 = 0 Solving -1.52 + -2y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.38 + -0.5y + y2 = 0 Move the constant term to the right: Add '0.38' to each side of the equation. -0.38 + -0.5y + 0.38 + y2 = 0 + 0.38 Reorder the terms: -0.38 + 0.38 + -0.5y + y2 = 0 + 0.38 Combine like terms: -0.38 + 0.38 = 0.00 0.00 + -0.5y + y2 = 0 + 0.38 -0.5y + y2 = 0 + 0.38 Combine like terms: 0 + 0.38 = 0.38 -0.5y + y2 = 0.38 The y term is -0.5y. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5y + 0.0625 + y2 = 0.38 + 0.0625 Reorder the terms: 0.0625 + -0.5y + y2 = 0.38 + 0.0625 Combine like terms: 0.38 + 0.0625 = 0.4425 0.0625 + -0.5y + y2 = 0.4425 Factor a perfect square on the left side: (y + -0.25)(y + -0.25) = 0.4425 Calculate the square root of the right side: 0.665206735 Break this problem into two subproblems by setting (y + -0.25) equal to 0.665206735 and -0.665206735.Subproblem 1
y + -0.25 = 0.665206735 Simplifying y + -0.25 = 0.665206735 Reorder the terms: -0.25 + y = 0.665206735 Solving -0.25 + y = 0.665206735 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = 0.665206735 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = 0.665206735 + 0.25 y = 0.665206735 + 0.25 Combine like terms: 0.665206735 + 0.25 = 0.915206735 y = 0.915206735 Simplifying y = 0.915206735Subproblem 2
y + -0.25 = -0.665206735 Simplifying y + -0.25 = -0.665206735 Reorder the terms: -0.25 + y = -0.665206735 Solving -0.25 + y = -0.665206735 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = -0.665206735 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = -0.665206735 + 0.25 y = -0.665206735 + 0.25 Combine like terms: -0.665206735 + 0.25 = -0.415206735 y = -0.415206735 Simplifying y = -0.415206735Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.915206735, -0.415206735}
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