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Simplifying 4y2 = -11y + 6 Reorder the terms: 4y2 = 6 + -11y Solving 4y2 = 6 + -11y Solving for variable 'y'. Reorder the terms: -6 + 11y + 4y2 = 6 + -11y + -6 + 11y Reorder the terms: -6 + 11y + 4y2 = 6 + -6 + -11y + 11y Combine like terms: 6 + -6 = 0 -6 + 11y + 4y2 = 0 + -11y + 11y -6 + 11y + 4y2 = -11y + 11y Combine like terms: -11y + 11y = 0 -6 + 11y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + 2.75y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 2.75y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 2.75y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 2.75y + y2 = 0 + 1.5 2.75y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 2.75y + y2 = 1.5 The y term is 2.75y. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75y + 1.890625 + y2 = 1.5 + 1.890625 Reorder the terms: 1.890625 + 2.75y + y2 = 1.5 + 1.890625 Combine like terms: 1.5 + 1.890625 = 3.390625 1.890625 + 2.75y + y2 = 3.390625 Factor a perfect square on the left side: (y + 1.375)(y + 1.375) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (y + 1.375) equal to 1.841364983 and -1.841364983.Subproblem 1
y + 1.375 = 1.841364983 Simplifying y + 1.375 = 1.841364983 Reorder the terms: 1.375 + y = 1.841364983 Solving 1.375 + y = 1.841364983 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + y = 1.841364983 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + y = 1.841364983 + -1.375 y = 1.841364983 + -1.375 Combine like terms: 1.841364983 + -1.375 = 0.466364983 y = 0.466364983 Simplifying y = 0.466364983Subproblem 2
y + 1.375 = -1.841364983 Simplifying y + 1.375 = -1.841364983 Reorder the terms: 1.375 + y = -1.841364983 Solving 1.375 + y = -1.841364983 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + y = -1.841364983 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + y = -1.841364983 + -1.375 y = -1.841364983 + -1.375 Combine like terms: -1.841364983 + -1.375 = -3.216364983 y = -3.216364983 Simplifying y = -3.216364983Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.466364983, -3.216364983}
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