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Simplifying 20y2 + 43y + -57 = 0 Reorder the terms: -57 + 43y + 20y2 = 0 Solving -57 + 43y + 20y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -2.85 + 2.15y + y2 = 0 Move the constant term to the right: Add '2.85' to each side of the equation. -2.85 + 2.15y + 2.85 + y2 = 0 + 2.85 Reorder the terms: -2.85 + 2.85 + 2.15y + y2 = 0 + 2.85 Combine like terms: -2.85 + 2.85 = 0.00 0.00 + 2.15y + y2 = 0 + 2.85 2.15y + y2 = 0 + 2.85 Combine like terms: 0 + 2.85 = 2.85 2.15y + y2 = 2.85 The y term is 2.15y. Take half its coefficient (1.075). Square it (1.155625) and add it to both sides. Add '1.155625' to each side of the equation. 2.15y + 1.155625 + y2 = 2.85 + 1.155625 Reorder the terms: 1.155625 + 2.15y + y2 = 2.85 + 1.155625 Combine like terms: 2.85 + 1.155625 = 4.005625 1.155625 + 2.15y + y2 = 4.005625 Factor a perfect square on the left side: (y + 1.075)(y + 1.075) = 4.005625 Calculate the square root of the right side: 2.001405756 Break this problem into two subproblems by setting (y + 1.075) equal to 2.001405756 and -2.001405756.Subproblem 1
y + 1.075 = 2.001405756 Simplifying y + 1.075 = 2.001405756 Reorder the terms: 1.075 + y = 2.001405756 Solving 1.075 + y = 2.001405756 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.075' to each side of the equation. 1.075 + -1.075 + y = 2.001405756 + -1.075 Combine like terms: 1.075 + -1.075 = 0.000 0.000 + y = 2.001405756 + -1.075 y = 2.001405756 + -1.075 Combine like terms: 2.001405756 + -1.075 = 0.926405756 y = 0.926405756 Simplifying y = 0.926405756Subproblem 2
y + 1.075 = -2.001405756 Simplifying y + 1.075 = -2.001405756 Reorder the terms: 1.075 + y = -2.001405756 Solving 1.075 + y = -2.001405756 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.075' to each side of the equation. 1.075 + -1.075 + y = -2.001405756 + -1.075 Combine like terms: 1.075 + -1.075 = 0.000 0.000 + y = -2.001405756 + -1.075 y = -2.001405756 + -1.075 Combine like terms: -2.001405756 + -1.075 = -3.076405756 y = -3.076405756 Simplifying y = -3.076405756Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.926405756, -3.076405756}
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