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Simplifying 5y2 + -24y + -28 = 0 Reorder the terms: -28 + -24y + 5y2 = 0 Solving -28 + -24y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.6 + -4.8y + y2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -4.8y + 5.6 + y2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -4.8y + y2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -4.8y + y2 = 0 + 5.6 -4.8y + y2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -4.8y + y2 = 5.6 The y term is -4.8y. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8y + 5.76 + y2 = 5.6 + 5.76 Reorder the terms: 5.76 + -4.8y + y2 = 5.6 + 5.76 Combine like terms: 5.6 + 5.76 = 11.36 5.76 + -4.8y + y2 = 11.36 Factor a perfect square on the left side: (y + -2.4)(y + -2.4) = 11.36 Calculate the square root of the right side: 3.370459909 Break this problem into two subproblems by setting (y + -2.4) equal to 3.370459909 and -3.370459909.Subproblem 1
y + -2.4 = 3.370459909 Simplifying y + -2.4 = 3.370459909 Reorder the terms: -2.4 + y = 3.370459909 Solving -2.4 + y = 3.370459909 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + y = 3.370459909 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + y = 3.370459909 + 2.4 y = 3.370459909 + 2.4 Combine like terms: 3.370459909 + 2.4 = 5.770459909 y = 5.770459909 Simplifying y = 5.770459909Subproblem 2
y + -2.4 = -3.370459909 Simplifying y + -2.4 = -3.370459909 Reorder the terms: -2.4 + y = -3.370459909 Solving -2.4 + y = -3.370459909 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + y = -3.370459909 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + y = -3.370459909 + 2.4 y = -3.370459909 + 2.4 Combine like terms: -3.370459909 + 2.4 = -0.970459909 y = -0.970459909 Simplifying y = -0.970459909Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.770459909, -0.970459909}
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