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Simplifying 84x2 + -384x + -192 = 0 Reorder the terms: -192 + -384x + 84x2 = 0 Solving -192 + -384x + 84x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-16 + -32x + 7x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-16 + -32x + 7x2)' equal to zero and attempt to solve: Simplifying -16 + -32x + 7x2 = 0 Solving -16 + -32x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + -4.571428571x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + -4.571428571x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + -4.571428571x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + -4.571428571x + x2 = 0 + 2.285714286 -4.571428571x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 -4.571428571x + x2 = 2.285714286 The x term is -4.571428571x. Take half its coefficient (-2.285714286). Square it (5.224489797) and add it to both sides. Add '5.224489797' to each side of the equation. -4.571428571x + 5.224489797 + x2 = 2.285714286 + 5.224489797 Reorder the terms: 5.224489797 + -4.571428571x + x2 = 2.285714286 + 5.224489797 Combine like terms: 2.285714286 + 5.224489797 = 7.510204083 5.224489797 + -4.571428571x + x2 = 7.510204083 Factor a perfect square on the left side: (x + -2.285714286)(x + -2.285714286) = 7.510204083 Calculate the square root of the right side: 2.740475156 Break this problem into two subproblems by setting (x + -2.285714286) equal to 2.740475156 and -2.740475156.Subproblem 1
x + -2.285714286 = 2.740475156 Simplifying x + -2.285714286 = 2.740475156 Reorder the terms: -2.285714286 + x = 2.740475156 Solving -2.285714286 + x = 2.740475156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.285714286' to each side of the equation. -2.285714286 + 2.285714286 + x = 2.740475156 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = 2.740475156 + 2.285714286 x = 2.740475156 + 2.285714286 Combine like terms: 2.740475156 + 2.285714286 = 5.026189442 x = 5.026189442 Simplifying x = 5.026189442Subproblem 2
x + -2.285714286 = -2.740475156 Simplifying x + -2.285714286 = -2.740475156 Reorder the terms: -2.285714286 + x = -2.740475156 Solving -2.285714286 + x = -2.740475156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.285714286' to each side of the equation. -2.285714286 + 2.285714286 + x = -2.740475156 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = -2.740475156 + 2.285714286 x = -2.740475156 + 2.285714286 Combine like terms: -2.740475156 + 2.285714286 = -0.45476087 x = -0.45476087 Simplifying x = -0.45476087Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.026189442, -0.45476087}Solution
x = {5.026189442, -0.45476087}
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