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Simplifying (G + -11)(G + -8) = 35 Reorder the terms: (-11 + G)(G + -8) = 35 Reorder the terms: (-11 + G)(-8 + G) = 35 Multiply (-11 + G) * (-8 + G) (-11(-8 + G) + G(-8 + G)) = 35 ((-8 * -11 + G * -11) + G(-8 + G)) = 35 ((88 + -11G) + G(-8 + G)) = 35 (88 + -11G + (-8 * G + G * G)) = 35 (88 + -11G + (-8G + G2)) = 35 Combine like terms: -11G + -8G = -19G (88 + -19G + G2) = 35 Solving 88 + -19G + G2 = 35 Solving for variable 'G'. Reorder the terms: 88 + -35 + -19G + G2 = 35 + -35 Combine like terms: 88 + -35 = 53 53 + -19G + G2 = 35 + -35 Combine like terms: 35 + -35 = 0 53 + -19G + G2 = 0 Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + -19G + -53 + G2 = 0 + -53 Reorder the terms: 53 + -53 + -19G + G2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + -19G + G2 = 0 + -53 -19G + G2 = 0 + -53 Combine like terms: 0 + -53 = -53 -19G + G2 = -53 The G term is -19G. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19G + 90.25 + G2 = -53 + 90.25 Reorder the terms: 90.25 + -19G + G2 = -53 + 90.25 Combine like terms: -53 + 90.25 = 37.25 90.25 + -19G + G2 = 37.25 Factor a perfect square on the left side: (G + -9.5)(G + -9.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (G + -9.5) equal to 6.103277808 and -6.103277808.Subproblem 1
G + -9.5 = 6.103277808 Simplifying G + -9.5 = 6.103277808 Reorder the terms: -9.5 + G = 6.103277808 Solving -9.5 + G = 6.103277808 Solving for variable 'G'. Move all terms containing G to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + G = 6.103277808 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + G = 6.103277808 + 9.5 G = 6.103277808 + 9.5 Combine like terms: 6.103277808 + 9.5 = 15.603277808 G = 15.603277808 Simplifying G = 15.603277808Subproblem 2
G + -9.5 = -6.103277808 Simplifying G + -9.5 = -6.103277808 Reorder the terms: -9.5 + G = -6.103277808 Solving -9.5 + G = -6.103277808 Solving for variable 'G'. Move all terms containing G to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + G = -6.103277808 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + G = -6.103277808 + 9.5 G = -6.103277808 + 9.5 Combine like terms: -6.103277808 + 9.5 = 3.396722192 G = 3.396722192 Simplifying G = 3.396722192Solution
The solution to the problem is based on the solutions from the subproblems. G = {15.603277808, 3.396722192}
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