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Simplifying 5y + 4y(y + -7) = 4(y + 2) + -4 Reorder the terms: 5y + 4y(-7 + y) = 4(y + 2) + -4 5y + (-7 * 4y + y * 4y) = 4(y + 2) + -4 5y + (-28y + 4y2) = 4(y + 2) + -4 Combine like terms: 5y + -28y = -23y -23y + 4y2 = 4(y + 2) + -4 Reorder the terms: -23y + 4y2 = 4(2 + y) + -4 -23y + 4y2 = (2 * 4 + y * 4) + -4 -23y + 4y2 = (8 + 4y) + -4 Reorder the terms: -23y + 4y2 = 8 + -4 + 4y Combine like terms: 8 + -4 = 4 -23y + 4y2 = 4 + 4y Solving -23y + 4y2 = 4 + 4y Solving for variable 'y'. Reorder the terms: -4 + -23y + -4y + 4y2 = 4 + 4y + -4 + -4y Combine like terms: -23y + -4y = -27y -4 + -27y + 4y2 = 4 + 4y + -4 + -4y Reorder the terms: -4 + -27y + 4y2 = 4 + -4 + 4y + -4y Combine like terms: 4 + -4 = 0 -4 + -27y + 4y2 = 0 + 4y + -4y -4 + -27y + 4y2 = 4y + -4y Combine like terms: 4y + -4y = 0 -4 + -27y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -6.75y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6.75y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -6.75y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6.75y + y2 = 0 + 1 -6.75y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6.75y + y2 = 1 The y term is -6.75y. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75y + 11.390625 + y2 = 1 + 11.390625 Reorder the terms: 11.390625 + -6.75y + y2 = 1 + 11.390625 Combine like terms: 1 + 11.390625 = 12.390625 11.390625 + -6.75y + y2 = 12.390625 Factor a perfect square on the left side: (y + -3.375)(y + -3.375) = 12.390625 Calculate the square root of the right side: 3.52003196 Break this problem into two subproblems by setting (y + -3.375) equal to 3.52003196 and -3.52003196.Subproblem 1
y + -3.375 = 3.52003196 Simplifying y + -3.375 = 3.52003196 Reorder the terms: -3.375 + y = 3.52003196 Solving -3.375 + y = 3.52003196 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + y = 3.52003196 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + y = 3.52003196 + 3.375 y = 3.52003196 + 3.375 Combine like terms: 3.52003196 + 3.375 = 6.89503196 y = 6.89503196 Simplifying y = 6.89503196Subproblem 2
y + -3.375 = -3.52003196 Simplifying y + -3.375 = -3.52003196 Reorder the terms: -3.375 + y = -3.52003196 Solving -3.375 + y = -3.52003196 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + y = -3.52003196 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + y = -3.52003196 + 3.375 y = -3.52003196 + 3.375 Combine like terms: -3.52003196 + 3.375 = -0.14503196 y = -0.14503196 Simplifying y = -0.14503196Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.89503196, -0.14503196}
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