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Simplifying 6.25y2 + -15y + 9 = 0 Reorder the terms: 9 + -15y + 6.25y2 = 0 Solving 9 + -15y + 6.25y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6.25 the coefficient of the squared term: Divide each side by '6.25'. 1.44 + -2.4y + y2 = 0 Move the constant term to the right: Add '-1.44' to each side of the equation. 1.44 + -2.4y + -1.44 + y2 = 0 + -1.44 Reorder the terms: 1.44 + -1.44 + -2.4y + y2 = 0 + -1.44 Combine like terms: 1.44 + -1.44 = 0.00 0.00 + -2.4y + y2 = 0 + -1.44 -2.4y + y2 = 0 + -1.44 Combine like terms: 0 + -1.44 = -1.44 -2.4y + y2 = -1.44 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 = -1.44 + 1.44 Reorder the terms: 1.44 + -2.4y + y2 = -1.44 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 1.44 + -2.4y + y2 = 0.00 Factor a perfect square on the left side: (y + -1.2)(y + -1.2) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (y + -1.2) equal to 0.00 and 0.00.Subproblem 1
y + -1.2 = 0.00 Simplifying y + -1.2 = 0.00 Reorder the terms: -1.2 + y = 0.00 Solving -1.2 + y = 0.00 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 = 0.00 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + y = 0.00 + 1.2 y = 0.00 + 1.2 Combine like terms: 0.00 + 1.2 = 1.2 y = 1.2 Simplifying y = 1.2Subproblem 2
y + -1.2 = 0.00 Simplifying y + -1.2 = 0.00 Reorder the terms: -1.2 + y = 0.00 Solving -1.2 + y = 0.00 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 = 0.00 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + y = 0.00 + 1.2 y = 0.00 + 1.2 Combine like terms: 0.00 + 1.2 = 1.2 y = 1.2 Simplifying y = 1.2Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.2, 1.2}
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