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Simplifying 45 = (x + 8)(3x + -3) Reorder the terms: 45 = (8 + x)(3x + -3) Reorder the terms: 45 = (8 + x)(-3 + 3x) Multiply (8 + x) * (-3 + 3x) 45 = (8(-3 + 3x) + x(-3 + 3x)) 45 = ((-3 * 8 + 3x * 8) + x(-3 + 3x)) 45 = ((-24 + 24x) + x(-3 + 3x)) 45 = (-24 + 24x + (-3 * x + 3x * x)) 45 = (-24 + 24x + (-3x + 3x2)) Combine like terms: 24x + -3x = 21x 45 = (-24 + 21x + 3x2) Solving 45 = -24 + 21x + 3x2 Solving for variable 'x'. Combine like terms: 45 + 24 = 69 69 + -21x + -3x2 = -24 + 21x + 3x2 + 24 + -21x + -3x2 Reorder the terms: 69 + -21x + -3x2 = -24 + 24 + 21x + -21x + 3x2 + -3x2 Combine like terms: -24 + 24 = 0 69 + -21x + -3x2 = 0 + 21x + -21x + 3x2 + -3x2 69 + -21x + -3x2 = 21x + -21x + 3x2 + -3x2 Combine like terms: 21x + -21x = 0 69 + -21x + -3x2 = 0 + 3x2 + -3x2 69 + -21x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 69 + -21x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(23 + -7x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(23 + -7x + -1x2)' equal to zero and attempt to solve: Simplifying 23 + -7x + -1x2 = 0 Solving 23 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23 + 7x + x2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + 7x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 7x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 7x + x2 = 0 + 23 7x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 7x + x2 = 23 The x term is 7x. 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. 7x + 12.25 + x2 = 23 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 23 + 12.25 Combine like terms: 23 + 12.25 = 35.25 12.25 + 7x + x2 = 35.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + 3.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + 3.5 = 5.937171044 Simplifying x + 3.5 = 5.937171044 Reorder the terms: 3.5 + x = 5.937171044 Solving 3.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 5.937171044 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.937171044 + -3.5 x = 5.937171044 + -3.5 Combine like terms: 5.937171044 + -3.5 = 2.437171044 x = 2.437171044 Simplifying x = 2.437171044Subproblem 2
x + 3.5 = -5.937171044 Simplifying x + 3.5 = -5.937171044 Reorder the terms: 3.5 + x = -5.937171044 Solving 3.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -5.937171044 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.937171044 + -3.5 x = -5.937171044 + -3.5 Combine like terms: -5.937171044 + -3.5 = -9.437171044 x = -9.437171044 Simplifying x = -9.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.437171044, -9.437171044}Solution
x = {2.437171044, -9.437171044}
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