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Simplifying 8y2 + -1y + 102y + 4 = y + 10 Reorder the terms: 4 + -1y + 102y + 8y2 = y + 10 Combine like terms: -1y + 102y = 101y 4 + 101y + 8y2 = y + 10 Reorder the terms: 4 + 101y + 8y2 = 10 + y Solving 4 + 101y + 8y2 = 10 + y Solving for variable 'y'. Reorder the terms: 4 + -10 + 101y + -1y + 8y2 = 10 + y + -10 + -1y Combine like terms: 4 + -10 = -6 -6 + 101y + -1y + 8y2 = 10 + y + -10 + -1y Combine like terms: 101y + -1y = 100y -6 + 100y + 8y2 = 10 + y + -10 + -1y Reorder the terms: -6 + 100y + 8y2 = 10 + -10 + y + -1y Combine like terms: 10 + -10 = 0 -6 + 100y + 8y2 = 0 + y + -1y -6 + 100y + 8y2 = y + -1y Combine like terms: y + -1y = 0 -6 + 100y + 8y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 50y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 50y + 4y2)' equal to zero and attempt to solve: Simplifying -3 + 50y + 4y2 = 0 Solving -3 + 50y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 12.5y + y2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 12.5y + 0.75 + y2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 12.5y + y2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 12.5y + y2 = 0 + 0.75 12.5y + y2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 12.5y + y2 = 0.75 The y term is 12.5y. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5y + 39.0625 + y2 = 0.75 + 39.0625 Reorder the terms: 39.0625 + 12.5y + y2 = 0.75 + 39.0625 Combine like terms: 0.75 + 39.0625 = 39.8125 39.0625 + 12.5y + y2 = 39.8125 Factor a perfect square on the left side: (y + 6.25)(y + 6.25) = 39.8125 Calculate the square root of the right side: 6.309714732 Break this problem into two subproblems by setting (y + 6.25) equal to 6.309714732 and -6.309714732.Subproblem 1
y + 6.25 = 6.309714732 Simplifying y + 6.25 = 6.309714732 Reorder the terms: 6.25 + y = 6.309714732 Solving 6.25 + y = 6.309714732 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + y = 6.309714732 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + y = 6.309714732 + -6.25 y = 6.309714732 + -6.25 Combine like terms: 6.309714732 + -6.25 = 0.059714732 y = 0.059714732 Simplifying y = 0.059714732Subproblem 2
y + 6.25 = -6.309714732 Simplifying y + 6.25 = -6.309714732 Reorder the terms: 6.25 + y = -6.309714732 Solving 6.25 + y = -6.309714732 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + y = -6.309714732 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + y = -6.309714732 + -6.25 y = -6.309714732 + -6.25 Combine like terms: -6.309714732 + -6.25 = -12.559714732 y = -12.559714732 Simplifying y = -12.559714732Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.059714732, -12.559714732}Solution
y = {0.059714732, -12.559714732}
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