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Simplifying 5y2 + -4y + 4 = 11 Reorder the terms: 4 + -4y + 5y2 = 11 Solving 4 + -4y + 5y2 = 11 Solving for variable 'y'. Reorder the terms: 4 + -11 + -4y + 5y2 = 11 + -11 Combine like terms: 4 + -11 = -7 -7 + -4y + 5y2 = 11 + -11 Combine like terms: 11 + -11 = 0 -7 + -4y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -0.8y + y2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.8y + 1.4 + y2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.8y + y2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.8y + y2 = 0 + 1.4 -0.8y + y2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.8y + y2 = 1.4 The y term is -0.8y. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8y + 0.16 + y2 = 1.4 + 0.16 Reorder the terms: 0.16 + -0.8y + y2 = 1.4 + 0.16 Combine like terms: 1.4 + 0.16 = 1.56 0.16 + -0.8y + y2 = 1.56 Factor a perfect square on the left side: (y + -0.4)(y + -0.4) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (y + -0.4) equal to 1.2489996 and -1.2489996.Subproblem 1
y + -0.4 = 1.2489996 Simplifying y + -0.4 = 1.2489996 Reorder the terms: -0.4 + y = 1.2489996 Solving -0.4 + y = 1.2489996 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + y = 1.2489996 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + y = 1.2489996 + 0.4 y = 1.2489996 + 0.4 Combine like terms: 1.2489996 + 0.4 = 1.6489996 y = 1.6489996 Simplifying y = 1.6489996Subproblem 2
y + -0.4 = -1.2489996 Simplifying y + -0.4 = -1.2489996 Reorder the terms: -0.4 + y = -1.2489996 Solving -0.4 + y = -1.2489996 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + y = -1.2489996 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + y = -1.2489996 + 0.4 y = -1.2489996 + 0.4 Combine like terms: -1.2489996 + 0.4 = -0.8489996 y = -0.8489996 Simplifying y = -0.8489996Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.6489996, -0.8489996}
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