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Simplifying 35 = (g + -11)(g + -8) Reorder the terms: 35 = (-11 + g)(g + -8) Reorder the terms: 35 = (-11 + g)(-8 + g) Multiply (-11 + g) * (-8 + g) 35 = (-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)) Combine like terms: -11g + -8g = -19g 35 = (88 + -19g + g2) Solving 35 = 88 + -19g + g2 Solving for variable 'g'. Combine like terms: 35 + -88 = -53 -53 + 19g + -1g2 = 88 + -19g + g2 + -88 + 19g + -1g2 Reorder the terms: -53 + 19g + -1g2 = 88 + -88 + -19g + 19g + g2 + -1g2 Combine like terms: 88 + -88 = 0 -53 + 19g + -1g2 = 0 + -19g + 19g + g2 + -1g2 -53 + 19g + -1g2 = -19g + 19g + g2 + -1g2 Combine like terms: -19g + 19g = 0 -53 + 19g + -1g2 = 0 + g2 + -1g2 -53 + 19g + -1g2 = g2 + -1g2 Combine like terms: g2 + -1g2 = 0 -53 + 19g + -1g2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 53 + -19g + g2 = 0 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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