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Simplifying 18.75 = y2 + -4y + 4 Reorder the terms: 18.75 = 4 + -4y + y2 Solving 18.75 = 4 + -4y + y2 Solving for variable 'y'. Combine like terms: 18.75 + -4 = 14.75 14.75 + 4y + -1y2 = 4 + -4y + y2 + -4 + 4y + -1y2 Reorder the terms: 14.75 + 4y + -1y2 = 4 + -4 + -4y + 4y + y2 + -1y2 Combine like terms: 4 + -4 = 0 14.75 + 4y + -1y2 = 0 + -4y + 4y + y2 + -1y2 14.75 + 4y + -1y2 = -4y + 4y + y2 + -1y2 Combine like terms: -4y + 4y = 0 14.75 + 4y + -1y2 = 0 + y2 + -1y2 14.75 + 4y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 14.75 + 4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14.75 + -4y + y2 = 0 Move the constant term to the right: Add '14.75' to each side of the equation. -14.75 + -4y + 14.75 + y2 = 0 + 14.75 Reorder the terms: -14.75 + 14.75 + -4y + y2 = 0 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + -4y + y2 = 0 + 14.75 -4y + y2 = 0 + 14.75 Combine like terms: 0 + 14.75 = 14.75 -4y + y2 = 14.75 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 14.75 + 4 Reorder the terms: 4 + -4y + y2 = 14.75 + 4 Combine like terms: 14.75 + 4 = 18.75 4 + -4y + y2 = 18.75 Factor a perfect square on the left side: (y + -2)(y + -2) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (y + -2) equal to 4.330127019 and -4.330127019.Subproblem 1
y + -2 = 4.330127019 Simplifying y + -2 = 4.330127019 Reorder the terms: -2 + y = 4.330127019 Solving -2 + y = 4.330127019 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 4.330127019 + 2 Combine like terms: -2 + 2 = 0 0 + y = 4.330127019 + 2 y = 4.330127019 + 2 Combine like terms: 4.330127019 + 2 = 6.330127019 y = 6.330127019 Simplifying y = 6.330127019Subproblem 2
y + -2 = -4.330127019 Simplifying y + -2 = -4.330127019 Reorder the terms: -2 + y = -4.330127019 Solving -2 + y = -4.330127019 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -4.330127019 + 2 Combine like terms: -2 + 2 = 0 0 + y = -4.330127019 + 2 y = -4.330127019 + 2 Combine like terms: -4.330127019 + 2 = -2.330127019 y = -2.330127019 Simplifying y = -2.330127019Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.330127019, -2.330127019}
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