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Simplifying 3x4 + -33x3 + 21x2 = 0 Reorder the terms: 21x2 + -33x3 + 3x4 = 0 Solving 21x2 + -33x3 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(7 + -11x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(7 + -11x + x2)' equal to zero and attempt to solve: Simplifying 7 + -11x + x2 = 0 Solving 7 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -11x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -11x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -11x + x2 = 0 + -7 -11x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -11x + x2 = -7 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -7 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -7 + 30.25 Combine like terms: -7 + 30.25 = 23.25 30.25 + -11x + x2 = 23.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (x + -5.5) equal to 4.82182538 and -4.82182538.Subproblem 1
x + -5.5 = 4.82182538 Simplifying x + -5.5 = 4.82182538 Reorder the terms: -5.5 + x = 4.82182538 Solving -5.5 + x = 4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 4.82182538 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 4.82182538 + 5.5 x = 4.82182538 + 5.5 Combine like terms: 4.82182538 + 5.5 = 10.32182538 x = 10.32182538 Simplifying x = 10.32182538Subproblem 2
x + -5.5 = -4.82182538 Simplifying x + -5.5 = -4.82182538 Reorder the terms: -5.5 + x = -4.82182538 Solving -5.5 + x = -4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -4.82182538 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -4.82182538 + 5.5 x = -4.82182538 + 5.5 Combine like terms: -4.82182538 + 5.5 = 0.67817462 x = 0.67817462 Simplifying x = 0.67817462Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.32182538, 0.67817462}Solution
x = {0, 10.32182538, 0.67817462}
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