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Simplifying 4y2 + -4y = 20 Reorder the terms: -4y + 4y2 = 20 Solving -4y + 4y2 = 20 Solving for variable 'y'. Reorder the terms: -20 + -4y + 4y2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -4y + 4y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -1y + y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -1y + y2)' equal to zero and attempt to solve: Simplifying -5 + -1y + y2 = 0 Solving -5 + -1y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -1y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + -1y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1y + y2 = 0 + 5 -1y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1y + y2 = 5 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 5 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + -1y + y2 = 5.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (y + -0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
y + -0.5 = 2.291287847 Simplifying y + -0.5 = 2.291287847 Reorder the terms: -0.5 + y = 2.291287847 Solving -0.5 + y = 2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 2.291287847 + 0.5 y = 2.291287847 + 0.5 Combine like terms: 2.291287847 + 0.5 = 2.791287847 y = 2.791287847 Simplifying y = 2.791287847Subproblem 2
y + -0.5 = -2.291287847 Simplifying y + -0.5 = -2.291287847 Reorder the terms: -0.5 + y = -2.291287847 Solving -0.5 + y = -2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -2.291287847 + 0.5 y = -2.291287847 + 0.5 Combine like terms: -2.291287847 + 0.5 = -1.791287847 y = -1.791287847 Simplifying y = -1.791287847Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.791287847, -1.791287847}Solution
y = {2.791287847, -1.791287847}
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