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Simplifying 4x3 + 8x2 + -22x = 0 Reorder the terms: -22x + 8x2 + 4x3 = 0 Solving -22x + 8x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-11 + 4x + 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 '(-11 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -11 + 4x + 2x2 = 0 Solving -11 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 2x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 2x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 2x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 2x + x2 = 0 + 5.5 2x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 2x + x2 = 5.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 5.5 + 1 Reorder the terms: 1 + 2x + x2 = 5.5 + 1 Combine like terms: 5.5 + 1 = 6.5 1 + 2x + x2 = 6.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + 1) equal to 2.549509757 and -2.549509757.Subproblem 1
x + 1 = 2.549509757 Simplifying x + 1 = 2.549509757 Reorder the terms: 1 + x = 2.549509757 Solving 1 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.549509757 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.549509757 + -1 x = 2.549509757 + -1 Combine like terms: 2.549509757 + -1 = 1.549509757 x = 1.549509757 Simplifying x = 1.549509757Subproblem 2
x + 1 = -2.549509757 Simplifying x + 1 = -2.549509757 Reorder the terms: 1 + x = -2.549509757 Solving 1 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.549509757 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.549509757 + -1 x = -2.549509757 + -1 Combine like terms: -2.549509757 + -1 = -3.549509757 x = -3.549509757 Simplifying x = -3.549509757Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.549509757, -3.549509757}Solution
x = {0, 1.549509757, -3.549509757}
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