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Simplifying 168 = 2(x + 7)(x + -3) Reorder the terms: 168 = 2(7 + x)(x + -3) Reorder the terms: 168 = 2(7 + x)(-3 + x) Multiply (7 + x) * (-3 + x) 168 = 2(7(-3 + x) + x(-3 + x)) 168 = 2((-3 * 7 + x * 7) + x(-3 + x)) 168 = 2((-21 + 7x) + x(-3 + x)) 168 = 2(-21 + 7x + (-3 * x + x * x)) 168 = 2(-21 + 7x + (-3x + x2)) Combine like terms: 7x + -3x = 4x 168 = 2(-21 + 4x + x2) 168 = (-21 * 2 + 4x * 2 + x2 * 2) 168 = (-42 + 8x + 2x2) Solving 168 = -42 + 8x + 2x2 Solving for variable 'x'. Combine like terms: 168 + 42 = 210 210 + -8x + -2x2 = -42 + 8x + 2x2 + 42 + -8x + -2x2 Reorder the terms: 210 + -8x + -2x2 = -42 + 42 + 8x + -8x + 2x2 + -2x2 Combine like terms: -42 + 42 = 0 210 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2 210 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 210 + -8x + -2x2 = 0 + 2x2 + -2x2 210 + -8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 210 + -8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(105 + -4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(105 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 105 + -4x + -1x2 = 0 Solving 105 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -105 + 4x + x2 = 0 Move the constant term to the right: Add '105' to each side of the equation. -105 + 4x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + 4x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 4x + x2 = 0 + 105 4x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 4x + x2 = 105 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 105 + 4 Reorder the terms: 4 + 4x + x2 = 105 + 4 Combine like terms: 105 + 4 = 109 4 + 4x + x2 = 109 Factor a perfect square on the left side: (x + 2)(x + 2) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + 2) equal to 10.440306509 and -10.440306509.Subproblem 1
x + 2 = 10.440306509 Simplifying x + 2 = 10.440306509 Reorder the terms: 2 + x = 10.440306509 Solving 2 + x = 10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 10.440306509 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10.440306509 + -2 x = 10.440306509 + -2 Combine like terms: 10.440306509 + -2 = 8.440306509 x = 8.440306509 Simplifying x = 8.440306509Subproblem 2
x + 2 = -10.440306509 Simplifying x + 2 = -10.440306509 Reorder the terms: 2 + x = -10.440306509 Solving 2 + x = -10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -10.440306509 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10.440306509 + -2 x = -10.440306509 + -2 Combine like terms: -10.440306509 + -2 = -12.440306509 x = -12.440306509 Simplifying x = -12.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.440306509, -12.440306509}Solution
x = {8.440306509, -12.440306509}
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