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Simplifying 42x2 + -4x + -56 = 0 Reorder the terms: -56 + -4x + 42x2 = 0 Solving -56 + -4x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + -2x + 21x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + -2x + 21x2)' equal to zero and attempt to solve: Simplifying -28 + -2x + 21x2 = 0 Solving -28 + -2x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.333333333 + -0.09523809524x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -0.09523809524x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -0.09523809524x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -0.09523809524x + x2 = 0 + 1.333333333 -0.09523809524x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -0.09523809524x + x2 = 1.333333333 The x term is -0.09523809524x. Take half its coefficient (-0.04761904762). Square it (0.002267573696) and add it to both sides. Add '0.002267573696' to each side of the equation. -0.09523809524x + 0.002267573696 + x2 = 1.333333333 + 0.002267573696 Reorder the terms: 0.002267573696 + -0.09523809524x + x2 = 1.333333333 + 0.002267573696 Combine like terms: 1.333333333 + 0.002267573696 = 1.335600906696 0.002267573696 + -0.09523809524x + x2 = 1.335600906696 Factor a perfect square on the left side: (x + -0.04761904762)(x + -0.04761904762) = 1.335600906696 Calculate the square root of the right side: 1.155682009 Break this problem into two subproblems by setting (x + -0.04761904762) equal to 1.155682009 and -1.155682009.Subproblem 1
x + -0.04761904762 = 1.155682009 Simplifying x + -0.04761904762 = 1.155682009 Reorder the terms: -0.04761904762 + x = 1.155682009 Solving -0.04761904762 + x = 1.155682009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04761904762' to each side of the equation. -0.04761904762 + 0.04761904762 + x = 1.155682009 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + x = 1.155682009 + 0.04761904762 x = 1.155682009 + 0.04761904762 Combine like terms: 1.155682009 + 0.04761904762 = 1.20330105662 x = 1.20330105662 Simplifying x = 1.20330105662Subproblem 2
x + -0.04761904762 = -1.155682009 Simplifying x + -0.04761904762 = -1.155682009 Reorder the terms: -0.04761904762 + x = -1.155682009 Solving -0.04761904762 + x = -1.155682009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04761904762' to each side of the equation. -0.04761904762 + 0.04761904762 + x = -1.155682009 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + x = -1.155682009 + 0.04761904762 x = -1.155682009 + 0.04761904762 Combine like terms: -1.155682009 + 0.04761904762 = -1.10806296138 x = -1.10806296138 Simplifying x = -1.10806296138Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.20330105662, -1.10806296138}Solution
x = {1.20330105662, -1.10806296138}
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