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Simplifying 8(14) = (x + 8)(2x + 8) Multiply 8 * 14 112 = (x + 8)(2x + 8) Reorder the terms: 112 = (8 + x)(2x + 8) Reorder the terms: 112 = (8 + x)(8 + 2x) Multiply (8 + x) * (8 + 2x) 112 = (8(8 + 2x) + x(8 + 2x)) 112 = ((8 * 8 + 2x * 8) + x(8 + 2x)) 112 = ((64 + 16x) + x(8 + 2x)) 112 = (64 + 16x + (8 * x + 2x * x)) 112 = (64 + 16x + (8x + 2x2)) Combine like terms: 16x + 8x = 24x 112 = (64 + 24x + 2x2) Solving 112 = 64 + 24x + 2x2 Solving for variable 'x'. Combine like terms: 112 + -64 = 48 48 + -24x + -2x2 = 64 + 24x + 2x2 + -64 + -24x + -2x2 Reorder the terms: 48 + -24x + -2x2 = 64 + -64 + 24x + -24x + 2x2 + -2x2 Combine like terms: 64 + -64 = 0 48 + -24x + -2x2 = 0 + 24x + -24x + 2x2 + -2x2 48 + -24x + -2x2 = 24x + -24x + 2x2 + -2x2 Combine like terms: 24x + -24x = 0 48 + -24x + -2x2 = 0 + 2x2 + -2x2 48 + -24x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 48 + -24x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -12x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -12x + -1x2)' equal to zero and attempt to solve: Simplifying 24 + -12x + -1x2 = 0 Solving 24 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + 12x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 12x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 12x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 12x + x2 = 0 + 24 12x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 12x + x2 = 24 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 24 + 36 Reorder the terms: 36 + 12x + x2 = 24 + 36 Combine like terms: 24 + 36 = 60 36 + 12x + x2 = 60 Factor a perfect square on the left side: (x + 6)(x + 6) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + 6) equal to 7.745966692 and -7.745966692.Subproblem 1
x + 6 = 7.745966692 Simplifying x + 6 = 7.745966692 Reorder the terms: 6 + x = 7.745966692 Solving 6 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 7.745966692 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.745966692 + -6 x = 7.745966692 + -6 Combine like terms: 7.745966692 + -6 = 1.745966692 x = 1.745966692 Simplifying x = 1.745966692Subproblem 2
x + 6 = -7.745966692 Simplifying x + 6 = -7.745966692 Reorder the terms: 6 + x = -7.745966692 Solving 6 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -7.745966692 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.745966692 + -6 x = -7.745966692 + -6 Combine like terms: -7.745966692 + -6 = -13.745966692 x = -13.745966692 Simplifying x = -13.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.745966692, -13.745966692}Solution
x = {1.745966692, -13.745966692}
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