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Simplifying y2 + -15y + 30 = 0 Reorder the terms: 30 + -15y + y2 = 0 Solving 30 + -15y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -15y + -30 + y2 = 0 + -30 Reorder the terms: 30 + -30 + -15y + y2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -15y + y2 = 0 + -30 -15y + y2 = 0 + -30 Combine like terms: 0 + -30 = -30 -15y + y2 = -30 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 = -30 + 56.25 Reorder the terms: 56.25 + -15y + y2 = -30 + 56.25 Combine like terms: -30 + 56.25 = 26.25 56.25 + -15y + y2 = 26.25 Factor a perfect square on the left side: (y + -7.5)(y + -7.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (y + -7.5) equal to 5.123475383 and -5.123475383.Subproblem 1
y + -7.5 = 5.123475383 Simplifying y + -7.5 = 5.123475383 Reorder the terms: -7.5 + y = 5.123475383 Solving -7.5 + y = 5.123475383 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 = 5.123475383 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = 5.123475383 + 7.5 y = 5.123475383 + 7.5 Combine like terms: 5.123475383 + 7.5 = 12.623475383 y = 12.623475383 Simplifying y = 12.623475383Subproblem 2
y + -7.5 = -5.123475383 Simplifying y + -7.5 = -5.123475383 Reorder the terms: -7.5 + y = -5.123475383 Solving -7.5 + y = -5.123475383 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 = -5.123475383 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = -5.123475383 + 7.5 y = -5.123475383 + 7.5 Combine like terms: -5.123475383 + 7.5 = 2.376524617 y = 2.376524617 Simplifying y = 2.376524617Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.623475383, 2.376524617}
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