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Simplifying 4y2 + 20y + -84 = 0 Reorder the terms: -84 + 20y + 4y2 = 0 Solving -84 + 20y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + 5y + y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-21 + 5y + y2)' equal to zero and attempt to solve: Simplifying -21 + 5y + y2 = 0 Solving -21 + 5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 5y + 21 + y2 = 0 + 21 Reorder the terms: -21 + 21 + 5y + y2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 5y + y2 = 0 + 21 5y + y2 = 0 + 21 Combine like terms: 0 + 21 = 21 5y + y2 = 21 The y term is 5y. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5y + 6.25 + y2 = 21 + 6.25 Reorder the terms: 6.25 + 5y + y2 = 21 + 6.25 Combine like terms: 21 + 6.25 = 27.25 6.25 + 5y + y2 = 27.25 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (y + 2.5) equal to 5.220153254 and -5.220153254.Subproblem 1
y + 2.5 = 5.220153254 Simplifying y + 2.5 = 5.220153254 Reorder the terms: 2.5 + y = 5.220153254 Solving 2.5 + y = 5.220153254 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = 5.220153254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 5.220153254 + -2.5 y = 5.220153254 + -2.5 Combine like terms: 5.220153254 + -2.5 = 2.720153254 y = 2.720153254 Simplifying y = 2.720153254Subproblem 2
y + 2.5 = -5.220153254 Simplifying y + 2.5 = -5.220153254 Reorder the terms: 2.5 + y = -5.220153254 Solving 2.5 + y = -5.220153254 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = -5.220153254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -5.220153254 + -2.5 y = -5.220153254 + -2.5 Combine like terms: -5.220153254 + -2.5 = -7.720153254 y = -7.720153254 Simplifying y = -7.720153254Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.720153254, -7.720153254}Solution
y = {2.720153254, -7.720153254}
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