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Simplifying 5y2 + -4y + -30 = 0 Reorder the terms: -30 + -4y + 5y2 = 0 Solving -30 + -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'. -6 + -0.8y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.8y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -0.8y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.8y + y2 = 0 + 6 -0.8y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.8y + y2 = 6 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 = 6 + 0.16 Reorder the terms: 0.16 + -0.8y + y2 = 6 + 0.16 Combine like terms: 6 + 0.16 = 6.16 0.16 + -0.8y + y2 = 6.16 Factor a perfect square on the left side: (y + -0.4)(y + -0.4) = 6.16 Calculate the square root of the right side: 2.481934729 Break this problem into two subproblems by setting (y + -0.4) equal to 2.481934729 and -2.481934729.Subproblem 1
y + -0.4 = 2.481934729 Simplifying y + -0.4 = 2.481934729 Reorder the terms: -0.4 + y = 2.481934729 Solving -0.4 + y = 2.481934729 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 = 2.481934729 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + y = 2.481934729 + 0.4 y = 2.481934729 + 0.4 Combine like terms: 2.481934729 + 0.4 = 2.881934729 y = 2.881934729 Simplifying y = 2.881934729Subproblem 2
y + -0.4 = -2.481934729 Simplifying y + -0.4 = -2.481934729 Reorder the terms: -0.4 + y = -2.481934729 Solving -0.4 + y = -2.481934729 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 = -2.481934729 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + y = -2.481934729 + 0.4 y = -2.481934729 + 0.4 Combine like terms: -2.481934729 + 0.4 = -2.081934729 y = -2.081934729 Simplifying y = -2.081934729Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.881934729, -2.081934729}
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