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Simplifying 10y2 + -11y = 3 Reorder the terms: -11y + 10y2 = 3 Solving -11y + 10y2 = 3 Solving for variable 'y'. Reorder the terms: -3 + -11y + 10y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -11y + 10y2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -1.1y + y2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -1.1y + 0.3 + y2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -1.1y + y2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -1.1y + y2 = 0 + 0.3 -1.1y + y2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -1.1y + y2 = 0.3 The y term is -1.1y. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1y + 0.3025 + y2 = 0.3 + 0.3025 Reorder the terms: 0.3025 + -1.1y + y2 = 0.3 + 0.3025 Combine like terms: 0.3 + 0.3025 = 0.6025 0.3025 + -1.1y + y2 = 0.6025 Factor a perfect square on the left side: (y + -0.55)(y + -0.55) = 0.6025 Calculate the square root of the right side: 0.776208735 Break this problem into two subproblems by setting (y + -0.55) equal to 0.776208735 and -0.776208735.Subproblem 1
y + -0.55 = 0.776208735 Simplifying y + -0.55 = 0.776208735 Reorder the terms: -0.55 + y = 0.776208735 Solving -0.55 + y = 0.776208735 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + y = 0.776208735 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + y = 0.776208735 + 0.55 y = 0.776208735 + 0.55 Combine like terms: 0.776208735 + 0.55 = 1.326208735 y = 1.326208735 Simplifying y = 1.326208735Subproblem 2
y + -0.55 = -0.776208735 Simplifying y + -0.55 = -0.776208735 Reorder the terms: -0.55 + y = -0.776208735 Solving -0.55 + y = -0.776208735 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + y = -0.776208735 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + y = -0.776208735 + 0.55 y = -0.776208735 + 0.55 Combine like terms: -0.776208735 + 0.55 = -0.226208735 y = -0.226208735 Simplifying y = -0.226208735Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.326208735, -0.226208735}
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