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Simplifying 4y2 + 19y + 5 = 0 Reorder the terms: 5 + 19y + 4y2 = 0 Solving 5 + 19y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 4.75y + y2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 4.75y + -1.25 + y2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 4.75y + y2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 4.75y + y2 = 0 + -1.25 4.75y + y2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 4.75y + y2 = -1.25 The y term is 4.75y. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75y + 5.640625 + y2 = -1.25 + 5.640625 Reorder the terms: 5.640625 + 4.75y + y2 = -1.25 + 5.640625 Combine like terms: -1.25 + 5.640625 = 4.390625 5.640625 + 4.75y + y2 = 4.390625 Factor a perfect square on the left side: (y + 2.375)(y + 2.375) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (y + 2.375) equal to 2.095381827 and -2.095381827.Subproblem 1
y + 2.375 = 2.095381827 Simplifying y + 2.375 = 2.095381827 Reorder the terms: 2.375 + y = 2.095381827 Solving 2.375 + y = 2.095381827 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + y = 2.095381827 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + y = 2.095381827 + -2.375 y = 2.095381827 + -2.375 Combine like terms: 2.095381827 + -2.375 = -0.279618173 y = -0.279618173 Simplifying y = -0.279618173Subproblem 2
y + 2.375 = -2.095381827 Simplifying y + 2.375 = -2.095381827 Reorder the terms: 2.375 + y = -2.095381827 Solving 2.375 + y = -2.095381827 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + y = -2.095381827 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + y = -2.095381827 + -2.375 y = -2.095381827 + -2.375 Combine like terms: -2.095381827 + -2.375 = -4.470381827 y = -4.470381827 Simplifying y = -4.470381827Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.279618173, -4.470381827}
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