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Simplifying 2y2 + -14y + 19 = 0 Reorder the terms: 19 + -14y + 2y2 = 0 Solving 19 + -14y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 9.5 + -7y + y2 = 0 Move the constant term to the right: Add '-9.5' to each side of the equation. 9.5 + -7y + -9.5 + y2 = 0 + -9.5 Reorder the terms: 9.5 + -9.5 + -7y + y2 = 0 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + -7y + y2 = 0 + -9.5 -7y + y2 = 0 + -9.5 Combine like terms: 0 + -9.5 = -9.5 -7y + y2 = -9.5 The y term is -7y. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y + 12.25 + y2 = -9.5 + 12.25 Reorder the terms: 12.25 + -7y + y2 = -9.5 + 12.25 Combine like terms: -9.5 + 12.25 = 2.75 12.25 + -7y + y2 = 2.75 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (y + -3.5) equal to 1.658312395 and -1.658312395.Subproblem 1
y + -3.5 = 1.658312395 Simplifying y + -3.5 = 1.658312395 Reorder the terms: -3.5 + y = 1.658312395 Solving -3.5 + y = 1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 1.658312395 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 1.658312395 + 3.5 y = 1.658312395 + 3.5 Combine like terms: 1.658312395 + 3.5 = 5.158312395 y = 5.158312395 Simplifying y = 5.158312395Subproblem 2
y + -3.5 = -1.658312395 Simplifying y + -3.5 = -1.658312395 Reorder the terms: -3.5 + y = -1.658312395 Solving -3.5 + y = -1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -1.658312395 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -1.658312395 + 3.5 y = -1.658312395 + 3.5 Combine like terms: -1.658312395 + 3.5 = 1.841687605 y = 1.841687605 Simplifying y = 1.841687605Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.158312395, 1.841687605}
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