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Simplifying 5y2 + -4y + -21 = 0 Reorder the terms: -21 + -4y + 5y2 = 0 Solving -21 + -4y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + -0.8y + y2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -0.8y + 4.2 + y2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -0.8y + y2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -0.8y + y2 = 0 + 4.2 -0.8y + y2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -0.8y + y2 = 4.2 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 = 4.2 + 0.16 Reorder the terms: 0.16 + -0.8y + y2 = 4.2 + 0.16 Combine like terms: 4.2 + 0.16 = 4.36 0.16 + -0.8y + y2 = 4.36 Factor a perfect square on the left side: (y + -0.4)(y + -0.4) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (y + -0.4) equal to 2.088061302 and -2.088061302.Subproblem 1
y + -0.4 = 2.088061302 Simplifying y + -0.4 = 2.088061302 Reorder the terms: -0.4 + y = 2.088061302 Solving -0.4 + y = 2.088061302 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 = 2.088061302 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + y = 2.088061302 + 0.4 y = 2.088061302 + 0.4 Combine like terms: 2.088061302 + 0.4 = 2.488061302 y = 2.488061302 Simplifying y = 2.488061302Subproblem 2
y + -0.4 = -2.088061302 Simplifying y + -0.4 = -2.088061302 Reorder the terms: -0.4 + y = -2.088061302 Solving -0.4 + y = -2.088061302 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 = -2.088061302 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + y = -2.088061302 + 0.4 y = -2.088061302 + 0.4 Combine like terms: -2.088061302 + 0.4 = -1.688061302 y = -1.688061302 Simplifying y = -1.688061302Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.488061302, -1.688061302}
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