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Simplifying y2 + -18y + 4 = 70 Reorder the terms: 4 + -18y + y2 = 70 Solving 4 + -18y + y2 = 70 Solving for variable 'y'. Reorder the terms: 4 + -70 + -18y + y2 = 70 + -70 Combine like terms: 4 + -70 = -66 -66 + -18y + y2 = 70 + -70 Combine like terms: 70 + -70 = 0 -66 + -18y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + -18y + 66 + y2 = 0 + 66 Reorder the terms: -66 + 66 + -18y + y2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + -18y + y2 = 0 + 66 -18y + y2 = 0 + 66 Combine like terms: 0 + 66 = 66 -18y + y2 = 66 The y term is -18y. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18y + 81 + y2 = 66 + 81 Reorder the terms: 81 + -18y + y2 = 66 + 81 Combine like terms: 66 + 81 = 147 81 + -18y + y2 = 147 Factor a perfect square on the left side: (y + -9)(y + -9) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (y + -9) equal to 12.124355653 and -12.124355653.Subproblem 1
y + -9 = 12.124355653 Simplifying y + -9 = 12.124355653 Reorder the terms: -9 + y = 12.124355653 Solving -9 + y = 12.124355653 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = 12.124355653 + 9 Combine like terms: -9 + 9 = 0 0 + y = 12.124355653 + 9 y = 12.124355653 + 9 Combine like terms: 12.124355653 + 9 = 21.124355653 y = 21.124355653 Simplifying y = 21.124355653Subproblem 2
y + -9 = -12.124355653 Simplifying y + -9 = -12.124355653 Reorder the terms: -9 + y = -12.124355653 Solving -9 + y = -12.124355653 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = -12.124355653 + 9 Combine like terms: -9 + 9 = 0 0 + y = -12.124355653 + 9 y = -12.124355653 + 9 Combine like terms: -12.124355653 + 9 = -3.124355653 y = -3.124355653 Simplifying y = -3.124355653Solution
The solution to the problem is based on the solutions from the subproblems. y = {21.124355653, -3.124355653}
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