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Simplifying (y2) + -1.5y + -7 = 0 y2 + -1.5y + -7 = 0 Reorder the terms: -7 + -1.5y + y2 = 0 Solving -7 + -1.5y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -1.5y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + -1.5y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1.5y + y2 = 0 + 7 -1.5y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1.5y + y2 = 7 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = 7 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = 7 + 0.5625 Combine like terms: 7 + 0.5625 = 7.5625 0.5625 + -1.5y + y2 = 7.5625 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = 7.5625 Calculate the square root of the right side: 2.75 Break this problem into two subproblems by setting (y + -0.75) equal to 2.75 and -2.75.Subproblem 1
y + -0.75 = 2.75 Simplifying y + -0.75 = 2.75 Reorder the terms: -0.75 + y = 2.75 Solving -0.75 + y = 2.75 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = 2.75 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 2.75 + 0.75 y = 2.75 + 0.75 Combine like terms: 2.75 + 0.75 = 3.5 y = 3.5 Simplifying y = 3.5Subproblem 2
y + -0.75 = -2.75 Simplifying y + -0.75 = -2.75 Reorder the terms: -0.75 + y = -2.75 Solving -0.75 + y = -2.75 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = -2.75 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -2.75 + 0.75 y = -2.75 + 0.75 Combine like terms: -2.75 + 0.75 = -2 y = -2 Simplifying y = -2Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.5, -2}
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