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Simplifying 2y2 + -10y = -7 Reorder the terms: -10y + 2y2 = -7 Solving -10y + 2y2 = -7 Solving for variable 'y'. Reorder the terms: 7 + -10y + 2y2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + -10y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -5y + y2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -5y + -3.5 + y2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -5y + y2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -5y + y2 = 0 + -3.5 -5y + y2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -5y + y2 = -3.5 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = -3.5 + 6.25 Reorder the terms: 6.25 + -5y + y2 = -3.5 + 6.25 Combine like terms: -3.5 + 6.25 = 2.75 6.25 + -5y + y2 = 2.75 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (y + -2.5) equal to 1.658312395 and -1.658312395.Subproblem 1
y + -2.5 = 1.658312395 Simplifying y + -2.5 = 1.658312395 Reorder the terms: -2.5 + y = 1.658312395 Solving -2.5 + y = 1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 1.658312395 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 1.658312395 + 2.5 y = 1.658312395 + 2.5 Combine like terms: 1.658312395 + 2.5 = 4.158312395 y = 4.158312395 Simplifying y = 4.158312395Subproblem 2
y + -2.5 = -1.658312395 Simplifying y + -2.5 = -1.658312395 Reorder the terms: -2.5 + y = -1.658312395 Solving -2.5 + y = -1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -1.658312395 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -1.658312395 + 2.5 y = -1.658312395 + 2.5 Combine like terms: -1.658312395 + 2.5 = 0.841687605 y = 0.841687605 Simplifying y = 0.841687605Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.158312395, 0.841687605}
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