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Simplifying 4y2 + 19y + -148 = 0 Reorder the terms: -148 + 19y + 4y2 = 0 Solving -148 + 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'. -37 + 4.75y + y2 = 0 Move the constant term to the right: Add '37' to each side of the equation. -37 + 4.75y + 37 + y2 = 0 + 37 Reorder the terms: -37 + 37 + 4.75y + y2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 4.75y + y2 = 0 + 37 4.75y + y2 = 0 + 37 Combine like terms: 0 + 37 = 37 4.75y + y2 = 37 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 = 37 + 5.640625 Reorder the terms: 5.640625 + 4.75y + y2 = 37 + 5.640625 Combine like terms: 37 + 5.640625 = 42.640625 5.640625 + 4.75y + y2 = 42.640625 Factor a perfect square on the left side: (y + 2.375)(y + 2.375) = 42.640625 Calculate the square root of the right side: 6.529978943 Break this problem into two subproblems by setting (y + 2.375) equal to 6.529978943 and -6.529978943.Subproblem 1
y + 2.375 = 6.529978943 Simplifying y + 2.375 = 6.529978943 Reorder the terms: 2.375 + y = 6.529978943 Solving 2.375 + y = 6.529978943 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 = 6.529978943 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + y = 6.529978943 + -2.375 y = 6.529978943 + -2.375 Combine like terms: 6.529978943 + -2.375 = 4.154978943 y = 4.154978943 Simplifying y = 4.154978943Subproblem 2
y + 2.375 = -6.529978943 Simplifying y + 2.375 = -6.529978943 Reorder the terms: 2.375 + y = -6.529978943 Solving 2.375 + y = -6.529978943 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 = -6.529978943 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + y = -6.529978943 + -2.375 y = -6.529978943 + -2.375 Combine like terms: -6.529978943 + -2.375 = -8.904978943 y = -8.904978943 Simplifying y = -8.904978943Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.154978943, -8.904978943}
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