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Simplifying 10y2 + 2y + -5 = 0 Reorder the terms: -5 + 2y + 10y2 = 0 Solving -5 + 2y + 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'. -0.5 + 0.2y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.2y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.2y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.2y + y2 = 0 + 0.5 0.2y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.2y + y2 = 0.5 The y term is 0.2y. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2y + 0.01 + y2 = 0.5 + 0.01 Reorder the terms: 0.01 + 0.2y + y2 = 0.5 + 0.01 Combine like terms: 0.5 + 0.01 = 0.51 0.01 + 0.2y + y2 = 0.51 Factor a perfect square on the left side: (y + 0.1)(y + 0.1) = 0.51 Calculate the square root of the right side: 0.714142843 Break this problem into two subproblems by setting (y + 0.1) equal to 0.714142843 and -0.714142843.Subproblem 1
y + 0.1 = 0.714142843 Simplifying y + 0.1 = 0.714142843 Reorder the terms: 0.1 + y = 0.714142843 Solving 0.1 + y = 0.714142843 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + y = 0.714142843 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + y = 0.714142843 + -0.1 y = 0.714142843 + -0.1 Combine like terms: 0.714142843 + -0.1 = 0.614142843 y = 0.614142843 Simplifying y = 0.614142843Subproblem 2
y + 0.1 = -0.714142843 Simplifying y + 0.1 = -0.714142843 Reorder the terms: 0.1 + y = -0.714142843 Solving 0.1 + y = -0.714142843 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + y = -0.714142843 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + y = -0.714142843 + -0.1 y = -0.714142843 + -0.1 Combine like terms: -0.714142843 + -0.1 = -0.814142843 y = -0.814142843 Simplifying y = -0.814142843Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.614142843, -0.814142843}
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