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Simplifying 4x3 + -26x2 + -42x = 0 Reorder the terms: -42x + -26x2 + 4x3 = 0 Solving -42x + -26x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-21 + -13x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-21 + -13x + 2x2)' equal to zero and attempt to solve: Simplifying -21 + -13x + 2x2 = 0 Solving -21 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -6.5x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -6.5x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -6.5x + x2 = 0 + 10.5 -6.5x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -6.5x + x2 = 10.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 10.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 10.5 + 10.5625 Combine like terms: 10.5 + 10.5625 = 21.0625 10.5625 + -6.5x + x2 = 21.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (x + -3.25) equal to 4.589389938 and -4.589389938.Subproblem 1
x + -3.25 = 4.589389938 Simplifying x + -3.25 = 4.589389938 Reorder the terms: -3.25 + x = 4.589389938 Solving -3.25 + x = 4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.589389938 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.589389938 + 3.25 x = 4.589389938 + 3.25 Combine like terms: 4.589389938 + 3.25 = 7.839389938 x = 7.839389938 Simplifying x = 7.839389938Subproblem 2
x + -3.25 = -4.589389938 Simplifying x + -3.25 = -4.589389938 Reorder the terms: -3.25 + x = -4.589389938 Solving -3.25 + x = -4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.589389938 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.589389938 + 3.25 x = -4.589389938 + 3.25 Combine like terms: -4.589389938 + 3.25 = -1.339389938 x = -1.339389938 Simplifying x = -1.339389938Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.839389938, -1.339389938}Solution
x = {0, 7.839389938, -1.339389938}
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