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Simplifying -10y2 + 3y = -9 Reorder the terms: 3y + -10y2 = -9 Solving 3y + -10y2 = -9 Solving for variable 'y'. Reorder the terms: 9 + 3y + -10y2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 3y + -10y2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.9 + -0.3y + y2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + -0.3y + 0.9 + y2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + -0.3y + y2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + -0.3y + y2 = 0 + 0.9 -0.3y + y2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 -0.3y + y2 = 0.9 The y term is -0.3y. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3y + 0.0225 + y2 = 0.9 + 0.0225 Reorder the terms: 0.0225 + -0.3y + y2 = 0.9 + 0.0225 Combine like terms: 0.9 + 0.0225 = 0.9225 0.0225 + -0.3y + y2 = 0.9225 Factor a perfect square on the left side: (y + -0.15)(y + -0.15) = 0.9225 Calculate the square root of the right side: 0.960468636 Break this problem into two subproblems by setting (y + -0.15) equal to 0.960468636 and -0.960468636.Subproblem 1
y + -0.15 = 0.960468636 Simplifying y + -0.15 = 0.960468636 Reorder the terms: -0.15 + y = 0.960468636 Solving -0.15 + y = 0.960468636 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + y = 0.960468636 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + y = 0.960468636 + 0.15 y = 0.960468636 + 0.15 Combine like terms: 0.960468636 + 0.15 = 1.110468636 y = 1.110468636 Simplifying y = 1.110468636Subproblem 2
y + -0.15 = -0.960468636 Simplifying y + -0.15 = -0.960468636 Reorder the terms: -0.15 + y = -0.960468636 Solving -0.15 + y = -0.960468636 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + y = -0.960468636 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + y = -0.960468636 + 0.15 y = -0.960468636 + 0.15 Combine like terms: -0.960468636 + 0.15 = -0.810468636 y = -0.810468636 Simplifying y = -0.810468636Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.110468636, -0.810468636}
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