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Simplifying (2x + 14)(x + -3) = 168 Reorder the terms: (14 + 2x)(x + -3) = 168 Reorder the terms: (14 + 2x)(-3 + x) = 168 Multiply (14 + 2x) * (-3 + x) (14(-3 + x) + 2x * (-3 + x)) = 168 ((-3 * 14 + x * 14) + 2x * (-3 + x)) = 168 ((-42 + 14x) + 2x * (-3 + x)) = 168 (-42 + 14x + (-3 * 2x + x * 2x)) = 168 (-42 + 14x + (-6x + 2x2)) = 168 Combine like terms: 14x + -6x = 8x (-42 + 8x + 2x2) = 168 Solving -42 + 8x + 2x2 = 168 Solving for variable 'x'. Reorder the terms: -42 + -168 + 8x + 2x2 = 168 + -168 Combine like terms: -42 + -168 = -210 -210 + 8x + 2x2 = 168 + -168 Combine like terms: 168 + -168 = 0 -210 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-105 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-105 + 4x + x2)' equal to zero and attempt to solve: Simplifying -105 + 4x + x2 = 0 Solving -105 + 4x + x2 = 0 Begin completing the square. 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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