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Simplifying 10y2 + 15y + 4 = 0 Reorder the terms: 4 + 15y + 10y2 = 0 Solving 4 + 15y + 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'. 0.4 + 1.5y + y2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 1.5y + -0.4 + y2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 1.5y + y2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 1.5y + y2 = 0 + -0.4 1.5y + y2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 1.5y + y2 = -0.4 The y term is 1.5y. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5y + 0.5625 + y2 = -0.4 + 0.5625 Reorder the terms: 0.5625 + 1.5y + y2 = -0.4 + 0.5625 Combine like terms: -0.4 + 0.5625 = 0.1625 0.5625 + 1.5y + y2 = 0.1625 Factor a perfect square on the left side: (y + 0.75)(y + 0.75) = 0.1625 Calculate the square root of the right side: 0.403112887 Break this problem into two subproblems by setting (y + 0.75) equal to 0.403112887 and -0.403112887.Subproblem 1
y + 0.75 = 0.403112887 Simplifying y + 0.75 = 0.403112887 Reorder the terms: 0.75 + y = 0.403112887 Solving 0.75 + y = 0.403112887 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = 0.403112887 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = 0.403112887 + -0.75 y = 0.403112887 + -0.75 Combine like terms: 0.403112887 + -0.75 = -0.346887113 y = -0.346887113 Simplifying y = -0.346887113Subproblem 2
y + 0.75 = -0.403112887 Simplifying y + 0.75 = -0.403112887 Reorder the terms: 0.75 + y = -0.403112887 Solving 0.75 + y = -0.403112887 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = -0.403112887 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = -0.403112887 + -0.75 y = -0.403112887 + -0.75 Combine like terms: -0.403112887 + -0.75 = -1.153112887 y = -1.153112887 Simplifying y = -1.153112887Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.346887113, -1.153112887}
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