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Simplifying y2 + 3y + -15 = 0 Reorder the terms: -15 + 3y + y2 = 0 Solving -15 + 3y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 3y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + 3y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 3y + y2 = 0 + 15 3y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 3y + y2 = 15 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = 15 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 15 + 2.25 Combine like terms: 15 + 2.25 = 17.25 2.25 + 3y + y2 = 17.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (y + 1.5) equal to 4.153311931 and -4.153311931.Subproblem 1
y + 1.5 = 4.153311931 Simplifying y + 1.5 = 4.153311931 Reorder the terms: 1.5 + y = 4.153311931 Solving 1.5 + y = 4.153311931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 4.153311931 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 4.153311931 + -1.5 y = 4.153311931 + -1.5 Combine like terms: 4.153311931 + -1.5 = 2.653311931 y = 2.653311931 Simplifying y = 2.653311931Subproblem 2
y + 1.5 = -4.153311931 Simplifying y + 1.5 = -4.153311931 Reorder the terms: 1.5 + y = -4.153311931 Solving 1.5 + y = -4.153311931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -4.153311931 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -4.153311931 + -1.5 y = -4.153311931 + -1.5 Combine like terms: -4.153311931 + -1.5 = -5.653311931 y = -5.653311931 Simplifying y = -5.653311931Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.653311931, -5.653311931}
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