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Simplifying 25y2 + 20y + -28 = 0 Reorder the terms: -28 + 20y + 25y2 = 0 Solving -28 + 20y + 25y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.12 + 0.8y + y2 = 0 Move the constant term to the right: Add '1.12' to each side of the equation. -1.12 + 0.8y + 1.12 + y2 = 0 + 1.12 Reorder the terms: -1.12 + 1.12 + 0.8y + y2 = 0 + 1.12 Combine like terms: -1.12 + 1.12 = 0.00 0.00 + 0.8y + y2 = 0 + 1.12 0.8y + y2 = 0 + 1.12 Combine like terms: 0 + 1.12 = 1.12 0.8y + y2 = 1.12 The y term is 0.8y. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8y + 0.16 + y2 = 1.12 + 0.16 Reorder the terms: 0.16 + 0.8y + y2 = 1.12 + 0.16 Combine like terms: 1.12 + 0.16 = 1.28 0.16 + 0.8y + y2 = 1.28 Factor a perfect square on the left side: (y + 0.4)(y + 0.4) = 1.28 Calculate the square root of the right side: 1.13137085 Break this problem into two subproblems by setting (y + 0.4) equal to 1.13137085 and -1.13137085.Subproblem 1
y + 0.4 = 1.13137085 Simplifying y + 0.4 = 1.13137085 Reorder the terms: 0.4 + y = 1.13137085 Solving 0.4 + y = 1.13137085 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = 1.13137085 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = 1.13137085 + -0.4 y = 1.13137085 + -0.4 Combine like terms: 1.13137085 + -0.4 = 0.73137085 y = 0.73137085 Simplifying y = 0.73137085Subproblem 2
y + 0.4 = -1.13137085 Simplifying y + 0.4 = -1.13137085 Reorder the terms: 0.4 + y = -1.13137085 Solving 0.4 + y = -1.13137085 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = -1.13137085 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = -1.13137085 + -0.4 y = -1.13137085 + -0.4 Combine like terms: -1.13137085 + -0.4 = -1.53137085 y = -1.53137085 Simplifying y = -1.53137085Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.73137085, -1.53137085}
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