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Simplifying 3x4 + 39x3 + 21x2 = 0 Reorder the terms: 21x2 + 39x3 + 3x4 = 0 Solving 21x2 + 39x3 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(7 + 13x + 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 + 13x + x2)' equal to zero and attempt to solve: Simplifying 7 + 13x + x2 = 0 Solving 7 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 13x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 13x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 13x + x2 = 0 + -7 13x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 13x + x2 = -7 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = -7 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -7 + 42.25 Combine like terms: -7 + 42.25 = 35.25 42.25 + 13x + x2 = 35.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + 6.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + 6.5 = 5.937171044 Simplifying x + 6.5 = 5.937171044 Reorder the terms: 6.5 + x = 5.937171044 Solving 6.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 5.937171044 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 5.937171044 + -6.5 x = 5.937171044 + -6.5 Combine like terms: 5.937171044 + -6.5 = -0.562828956 x = -0.562828956 Simplifying x = -0.562828956Subproblem 2
x + 6.5 = -5.937171044 Simplifying x + 6.5 = -5.937171044 Reorder the terms: 6.5 + x = -5.937171044 Solving 6.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -5.937171044 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -5.937171044 + -6.5 x = -5.937171044 + -6.5 Combine like terms: -5.937171044 + -6.5 = -12.437171044 x = -12.437171044 Simplifying x = -12.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.562828956, -12.437171044}Solution
x = {0, -0.562828956, -12.437171044}
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