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Simplifying 1 + -0.9y = 0.5y2 Solving 1 + -0.9y = 0.5y2 Solving for variable 'y'. Combine like terms: 0.5y2 + -0.5y2 = 0.0 1 + -0.9y + -0.5y2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -2 + 1.8y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.8y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + 1.8y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.8y + y2 = 0 + 2 1.8y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.8y + y2 = 2 The y term is 1.8y. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8y + 0.81 + y2 = 2 + 0.81 Reorder the terms: 0.81 + 1.8y + y2 = 2 + 0.81 Combine like terms: 2 + 0.81 = 2.81 0.81 + 1.8y + y2 = 2.81 Factor a perfect square on the left side: (y + 0.9)(y + 0.9) = 2.81 Calculate the square root of the right side: 1.676305461 Break this problem into two subproblems by setting (y + 0.9) equal to 1.676305461 and -1.676305461.Subproblem 1
y + 0.9 = 1.676305461 Simplifying y + 0.9 = 1.676305461 Reorder the terms: 0.9 + y = 1.676305461 Solving 0.9 + y = 1.676305461 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + y = 1.676305461 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + y = 1.676305461 + -0.9 y = 1.676305461 + -0.9 Combine like terms: 1.676305461 + -0.9 = 0.776305461 y = 0.776305461 Simplifying y = 0.776305461Subproblem 2
y + 0.9 = -1.676305461 Simplifying y + 0.9 = -1.676305461 Reorder the terms: 0.9 + y = -1.676305461 Solving 0.9 + y = -1.676305461 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + y = -1.676305461 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + y = -1.676305461 + -0.9 y = -1.676305461 + -0.9 Combine like terms: -1.676305461 + -0.9 = -2.576305461 y = -2.576305461 Simplifying y = -2.576305461Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.776305461, -2.576305461}
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