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Simplifying 15.2y + -1y2 = 52 Solving 15.2y + -1y2 = 52 Solving for variable 'y'. Reorder the terms: -52 + 15.2y + -1y2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 15.2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 52 + -15.2y + y2 = 0 Move the constant term to the right: Add '-52' to each side of the equation. 52 + -15.2y + -52 + y2 = 0 + -52 Reorder the terms: 52 + -52 + -15.2y + y2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -15.2y + y2 = 0 + -52 -15.2y + y2 = 0 + -52 Combine like terms: 0 + -52 = -52 -15.2y + y2 = -52 The y term is -15.2y. Take half its coefficient (-7.6). Square it (57.76) and add it to both sides. Add '57.76' to each side of the equation. -15.2y + 57.76 + y2 = -52 + 57.76 Reorder the terms: 57.76 + -15.2y + y2 = -52 + 57.76 Combine like terms: -52 + 57.76 = 5.76 57.76 + -15.2y + y2 = 5.76 Factor a perfect square on the left side: (y + -7.6)(y + -7.6) = 5.76 Calculate the square root of the right side: 2.4 Break this problem into two subproblems by setting (y + -7.6) equal to 2.4 and -2.4.Subproblem 1
y + -7.6 = 2.4 Simplifying y + -7.6 = 2.4 Reorder the terms: -7.6 + y = 2.4 Solving -7.6 + y = 2.4 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.6' to each side of the equation. -7.6 + 7.6 + y = 2.4 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + y = 2.4 + 7.6 y = 2.4 + 7.6 Combine like terms: 2.4 + 7.6 = 10 y = 10 Simplifying y = 10Subproblem 2
y + -7.6 = -2.4 Simplifying y + -7.6 = -2.4 Reorder the terms: -7.6 + y = -2.4 Solving -7.6 + y = -2.4 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.6' to each side of the equation. -7.6 + 7.6 + y = -2.4 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + y = -2.4 + 7.6 y = -2.4 + 7.6 Combine like terms: -2.4 + 7.6 = 5.2 y = 5.2 Simplifying y = 5.2Solution
The solution to the problem is based on the solutions from the subproblems. y = {10, 5.2}
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