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Simplifying 5y2 + -4y + -56 = 0 Reorder the terms: -56 + -4y + 5y2 = 0 Solving -56 + -4y + 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'. -11.2 + -0.8y + y2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + -0.8y + 11.2 + y2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + -0.8y + y2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + -0.8y + y2 = 0 + 11.2 -0.8y + y2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 -0.8y + y2 = 11.2 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 = 11.2 + 0.16 Reorder the terms: 0.16 + -0.8y + y2 = 11.2 + 0.16 Combine like terms: 11.2 + 0.16 = 11.36 0.16 + -0.8y + y2 = 11.36 Factor a perfect square on the left side: (y + -0.4)(y + -0.4) = 11.36 Calculate the square root of the right side: 3.370459909 Break this problem into two subproblems by setting (y + -0.4) equal to 3.370459909 and -3.370459909.Subproblem 1
y + -0.4 = 3.370459909 Simplifying y + -0.4 = 3.370459909 Reorder the terms: -0.4 + y = 3.370459909 Solving -0.4 + y = 3.370459909 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 = 3.370459909 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + y = 3.370459909 + 0.4 y = 3.370459909 + 0.4 Combine like terms: 3.370459909 + 0.4 = 3.770459909 y = 3.770459909 Simplifying y = 3.770459909Subproblem 2
y + -0.4 = -3.370459909 Simplifying y + -0.4 = -3.370459909 Reorder the terms: -0.4 + y = -3.370459909 Solving -0.4 + y = -3.370459909 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 = -3.370459909 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + y = -3.370459909 + 0.4 y = -3.370459909 + 0.4 Combine like terms: -3.370459909 + 0.4 = -2.970459909 y = -2.970459909 Simplifying y = -2.970459909Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.770459909, -2.970459909}
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