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Simplifying 6x + 2 = 4x(x + -7) Reorder the terms: 2 + 6x = 4x(x + -7) Reorder the terms: 2 + 6x = 4x(-7 + x) 2 + 6x = (-7 * 4x + x * 4x) 2 + 6x = (-28x + 4x2) Solving 2 + 6x = -28x + 4x2 Solving for variable 'x'. Combine like terms: 6x + 28x = 34x 2 + 34x + -4x2 = -28x + 4x2 + 28x + -4x2 Reorder the terms: 2 + 34x + -4x2 = -28x + 28x + 4x2 + -4x2 Combine like terms: -28x + 28x = 0 2 + 34x + -4x2 = 0 + 4x2 + -4x2 2 + 34x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 2 + 34x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 17x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 17x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + 17x + -2x2 = 0 Solving 1 + 17x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -8.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -8.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -8.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -8.5x + x2 = 0 + 0.5 -8.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -8.5x + x2 = 0.5 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 0.5 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 0.5 + 18.0625 Combine like terms: 0.5 + 18.0625 = 18.5625 18.0625 + -8.5x + x2 = 18.5625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (x + -4.25) equal to 4.308421985 and -4.308421985.Subproblem 1
x + -4.25 = 4.308421985 Simplifying x + -4.25 = 4.308421985 Reorder the terms: -4.25 + x = 4.308421985 Solving -4.25 + x = 4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.308421985 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.308421985 + 4.25 x = 4.308421985 + 4.25 Combine like terms: 4.308421985 + 4.25 = 8.558421985 x = 8.558421985 Simplifying x = 8.558421985Subproblem 2
x + -4.25 = -4.308421985 Simplifying x + -4.25 = -4.308421985 Reorder the terms: -4.25 + x = -4.308421985 Solving -4.25 + x = -4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.308421985 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.308421985 + 4.25 x = -4.308421985 + 4.25 Combine like terms: -4.308421985 + 4.25 = -0.058421985 x = -0.058421985 Simplifying x = -0.058421985Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.558421985, -0.058421985}Solution
x = {8.558421985, -0.058421985}
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