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Simplifying 10y2 + -18y + -10 = 0 Reorder the terms: -10 + -18y + 10y2 = 0 Solving -10 + -18y + 10y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -9y + 5y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -9y + 5y2)' equal to zero and attempt to solve: Simplifying -5 + -9y + 5y2 = 0 Solving -5 + -9y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -1.8y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.8y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -1.8y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.8y + y2 = 0 + 1 -1.8y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.8y + y2 = 1 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 = 1 + 0.81 Reorder the terms: 0.81 + -1.8y + y2 = 1 + 0.81 Combine like terms: 1 + 0.81 = 1.81 0.81 + -1.8y + y2 = 1.81 Factor a perfect square on the left side: (y + -0.9)(y + -0.9) = 1.81 Calculate the square root of the right side: 1.345362405 Break this problem into two subproblems by setting (y + -0.9) equal to 1.345362405 and -1.345362405.Subproblem 1
y + -0.9 = 1.345362405 Simplifying y + -0.9 = 1.345362405 Reorder the terms: -0.9 + y = 1.345362405 Solving -0.9 + y = 1.345362405 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 = 1.345362405 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + y = 1.345362405 + 0.9 y = 1.345362405 + 0.9 Combine like terms: 1.345362405 + 0.9 = 2.245362405 y = 2.245362405 Simplifying y = 2.245362405Subproblem 2
y + -0.9 = -1.345362405 Simplifying y + -0.9 = -1.345362405 Reorder the terms: -0.9 + y = -1.345362405 Solving -0.9 + y = -1.345362405 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 = -1.345362405 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + y = -1.345362405 + 0.9 y = -1.345362405 + 0.9 Combine like terms: -1.345362405 + 0.9 = -0.445362405 y = -0.445362405 Simplifying y = -0.445362405Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.245362405, -0.445362405}Solution
y = {2.245362405, -0.445362405}
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