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Simplifying 16y2 + -114y + 4 = 0 Reorder the terms: 4 + -114y + 16y2 = 0 Solving 4 + -114y + 16y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -57y + 8y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -57y + 8y2)' equal to zero and attempt to solve: Simplifying 2 + -57y + 8y2 = 0 Solving 2 + -57y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + -7.125y + y2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -7.125y + -0.25 + y2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -7.125y + y2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -7.125y + y2 = 0 + -0.25 -7.125y + y2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -7.125y + y2 = -0.25 The y term is -7.125y. Take half its coefficient (-3.5625). Square it (12.69140625) and add it to both sides. Add '12.69140625' to each side of the equation. -7.125y + 12.69140625 + y2 = -0.25 + 12.69140625 Reorder the terms: 12.69140625 + -7.125y + y2 = -0.25 + 12.69140625 Combine like terms: -0.25 + 12.69140625 = 12.44140625 12.69140625 + -7.125y + y2 = 12.44140625 Factor a perfect square on the left side: (y + -3.5625)(y + -3.5625) = 12.44140625 Calculate the square root of the right side: 3.527237765 Break this problem into two subproblems by setting (y + -3.5625) equal to 3.527237765 and -3.527237765.Subproblem 1
y + -3.5625 = 3.527237765 Simplifying y + -3.5625 = 3.527237765 Reorder the terms: -3.5625 + y = 3.527237765 Solving -3.5625 + y = 3.527237765 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5625' to each side of the equation. -3.5625 + 3.5625 + y = 3.527237765 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + y = 3.527237765 + 3.5625 y = 3.527237765 + 3.5625 Combine like terms: 3.527237765 + 3.5625 = 7.089737765 y = 7.089737765 Simplifying y = 7.089737765Subproblem 2
y + -3.5625 = -3.527237765 Simplifying y + -3.5625 = -3.527237765 Reorder the terms: -3.5625 + y = -3.527237765 Solving -3.5625 + y = -3.527237765 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5625' to each side of the equation. -3.5625 + 3.5625 + y = -3.527237765 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + y = -3.527237765 + 3.5625 y = -3.527237765 + 3.5625 Combine like terms: -3.527237765 + 3.5625 = 0.035262235 y = 0.035262235 Simplifying y = 0.035262235Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.089737765, 0.035262235}Solution
y = {7.089737765, 0.035262235}
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