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Simplifying 10y2 + -19y + -14 = 0 Reorder the terms: -14 + -19y + 10y2 = 0 Solving -14 + -19y + 10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.4 + -1.9y + y2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -1.9y + 1.4 + y2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -1.9y + y2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -1.9y + y2 = 0 + 1.4 -1.9y + y2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -1.9y + y2 = 1.4 The y term is -1.9y. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9y + 0.9025 + y2 = 1.4 + 0.9025 Reorder the terms: 0.9025 + -1.9y + y2 = 1.4 + 0.9025 Combine like terms: 1.4 + 0.9025 = 2.3025 0.9025 + -1.9y + y2 = 2.3025 Factor a perfect square on the left side: (y + -0.95)(y + -0.95) = 2.3025 Calculate the square root of the right side: 1.517399091 Break this problem into two subproblems by setting (y + -0.95) equal to 1.517399091 and -1.517399091.Subproblem 1
y + -0.95 = 1.517399091 Simplifying y + -0.95 = 1.517399091 Reorder the terms: -0.95 + y = 1.517399091 Solving -0.95 + y = 1.517399091 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + y = 1.517399091 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + y = 1.517399091 + 0.95 y = 1.517399091 + 0.95 Combine like terms: 1.517399091 + 0.95 = 2.467399091 y = 2.467399091 Simplifying y = 2.467399091Subproblem 2
y + -0.95 = -1.517399091 Simplifying y + -0.95 = -1.517399091 Reorder the terms: -0.95 + y = -1.517399091 Solving -0.95 + y = -1.517399091 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + y = -1.517399091 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + y = -1.517399091 + 0.95 y = -1.517399091 + 0.95 Combine like terms: -1.517399091 + 0.95 = -0.567399091 y = -0.567399091 Simplifying y = -0.567399091Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.467399091, -0.567399091}
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