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Simplifying 2y2 + -18y + -6 = y2 + -3y Reorder the terms: -6 + -18y + 2y2 = y2 + -3y Reorder the terms: -6 + -18y + 2y2 = -3y + y2 Solving -6 + -18y + 2y2 = -3y + y2 Solving for variable 'y'. Reorder the terms: -6 + -18y + 3y + 2y2 + -1y2 = -3y + y2 + 3y + -1y2 Combine like terms: -18y + 3y = -15y -6 + -15y + 2y2 + -1y2 = -3y + y2 + 3y + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 -6 + -15y + 1y2 = -3y + y2 + 3y + -1y2 Reorder the terms: -6 + -15y + 1y2 = -3y + 3y + y2 + -1y2 Combine like terms: -3y + 3y = 0 -6 + -15y + 1y2 = 0 + y2 + -1y2 -6 + -15y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -6 + -15y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -15y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -15y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -15y + y2 = 0 + 6 -15y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -15y + y2 = 6 The y term is -15y. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15y + 56.25 + y2 = 6 + 56.25 Reorder the terms: 56.25 + -15y + y2 = 6 + 56.25 Combine like terms: 6 + 56.25 = 62.25 56.25 + -15y + y2 = 62.25 Factor a perfect square on the left side: (y + -7.5)(y + -7.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (y + -7.5) equal to 7.889866919 and -7.889866919.Subproblem 1
y + -7.5 = 7.889866919 Simplifying y + -7.5 = 7.889866919 Reorder the terms: -7.5 + y = 7.889866919 Solving -7.5 + y = 7.889866919 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = 7.889866919 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = 7.889866919 + 7.5 y = 7.889866919 + 7.5 Combine like terms: 7.889866919 + 7.5 = 15.389866919 y = 15.389866919 Simplifying y = 15.389866919Subproblem 2
y + -7.5 = -7.889866919 Simplifying y + -7.5 = -7.889866919 Reorder the terms: -7.5 + y = -7.889866919 Solving -7.5 + y = -7.889866919 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = -7.889866919 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = -7.889866919 + 7.5 y = -7.889866919 + 7.5 Combine like terms: -7.889866919 + 7.5 = -0.389866919 y = -0.389866919 Simplifying y = -0.389866919Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.389866919, -0.389866919}
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