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Simplifying 25y2 + 60y + -29 = 0 Reorder the terms: -29 + 60y + 25y2 = 0 Solving -29 + 60y + 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'. -1.16 + 2.4y + y2 = 0 Move the constant term to the right: Add '1.16' to each side of the equation. -1.16 + 2.4y + 1.16 + y2 = 0 + 1.16 Reorder the terms: -1.16 + 1.16 + 2.4y + y2 = 0 + 1.16 Combine like terms: -1.16 + 1.16 = 0.00 0.00 + 2.4y + y2 = 0 + 1.16 2.4y + y2 = 0 + 1.16 Combine like terms: 0 + 1.16 = 1.16 2.4y + y2 = 1.16 The y term is 2.4y. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4y + 1.44 + y2 = 1.16 + 1.44 Reorder the terms: 1.44 + 2.4y + y2 = 1.16 + 1.44 Combine like terms: 1.16 + 1.44 = 2.6 1.44 + 2.4y + y2 = 2.6 Factor a perfect square on the left side: (y + 1.2)(y + 1.2) = 2.6 Calculate the square root of the right side: 1.61245155 Break this problem into two subproblems by setting (y + 1.2) equal to 1.61245155 and -1.61245155.Subproblem 1
y + 1.2 = 1.61245155 Simplifying y + 1.2 = 1.61245155 Reorder the terms: 1.2 + y = 1.61245155 Solving 1.2 + y = 1.61245155 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + y = 1.61245155 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + y = 1.61245155 + -1.2 y = 1.61245155 + -1.2 Combine like terms: 1.61245155 + -1.2 = 0.41245155 y = 0.41245155 Simplifying y = 0.41245155Subproblem 2
y + 1.2 = -1.61245155 Simplifying y + 1.2 = -1.61245155 Reorder the terms: 1.2 + y = -1.61245155 Solving 1.2 + y = -1.61245155 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + y = -1.61245155 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + y = -1.61245155 + -1.2 y = -1.61245155 + -1.2 Combine like terms: -1.61245155 + -1.2 = -2.81245155 y = -2.81245155 Simplifying y = -2.81245155Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.41245155, -2.81245155}
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