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Simplifying y2 + 3y + 10 = 70 Reorder the terms: 10 + 3y + y2 = 70 Solving 10 + 3y + y2 = 70 Solving for variable 'y'. Reorder the terms: 10 + -70 + 3y + y2 = 70 + -70 Combine like terms: 10 + -70 = -60 -60 + 3y + y2 = 70 + -70 Combine like terms: 70 + -70 = 0 -60 + 3y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 3y + 60 + y2 = 0 + 60 Reorder the terms: -60 + 60 + 3y + y2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 3y + y2 = 0 + 60 3y + y2 = 0 + 60 Combine like terms: 0 + 60 = 60 3y + y2 = 60 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 = 60 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 60 + 2.25 Combine like terms: 60 + 2.25 = 62.25 2.25 + 3y + y2 = 62.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (y + 1.5) equal to 7.889866919 and -7.889866919.Subproblem 1
y + 1.5 = 7.889866919 Simplifying y + 1.5 = 7.889866919 Reorder the terms: 1.5 + y = 7.889866919 Solving 1.5 + y = 7.889866919 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 = 7.889866919 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 7.889866919 + -1.5 y = 7.889866919 + -1.5 Combine like terms: 7.889866919 + -1.5 = 6.389866919 y = 6.389866919 Simplifying y = 6.389866919Subproblem 2
y + 1.5 = -7.889866919 Simplifying y + 1.5 = -7.889866919 Reorder the terms: 1.5 + y = -7.889866919 Solving 1.5 + y = -7.889866919 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 = -7.889866919 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -7.889866919 + -1.5 y = -7.889866919 + -1.5 Combine like terms: -7.889866919 + -1.5 = -9.389866919 y = -9.389866919 Simplifying y = -9.389866919Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.389866919, -9.389866919}
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