3x^4-21x^3=10x^2

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Solution for 3x^4-21x^3=10x^2 equation:


Simplifying
3x4 + -21x3 = 10x2

Reorder the terms:
-21x3 + 3x4 = 10x2

Solving
-21x3 + 3x4 = 10x2

Solving for variable 'x'.

Reorder the terms:
-10x2 + -21x3 + 3x4 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-10x2 + -21x3 + 3x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-10 + -21x + 3x2) = 0

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 '(-10 + -21x + 3x2)' equal to zero and attempt to solve: Simplifying -10 + -21x + 3x2 = 0 Solving -10 + -21x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -7x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -7x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -7x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -7x + x2 = 0 + 3.333333333 -7x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -7x + x2 = 3.333333333 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 3.333333333 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 3.333333333 + 12.25 Combine like terms: 3.333333333 + 12.25 = 15.583333333 12.25 + -7x + x2 = 15.583333333 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 15.583333333 Calculate the square root of the right side: 3.947573094 Break this problem into two subproblems by setting (x + -3.5) equal to 3.947573094 and -3.947573094.

Subproblem 1

x + -3.5 = 3.947573094 Simplifying x + -3.5 = 3.947573094 Reorder the terms: -3.5 + x = 3.947573094 Solving -3.5 + x = 3.947573094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.947573094 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.947573094 + 3.5 x = 3.947573094 + 3.5 Combine like terms: 3.947573094 + 3.5 = 7.447573094 x = 7.447573094 Simplifying x = 7.447573094

Subproblem 2

x + -3.5 = -3.947573094 Simplifying x + -3.5 = -3.947573094 Reorder the terms: -3.5 + x = -3.947573094 Solving -3.5 + x = -3.947573094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.947573094 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.947573094 + 3.5 x = -3.947573094 + 3.5 Combine like terms: -3.947573094 + 3.5 = -0.447573094 x = -0.447573094 Simplifying x = -0.447573094

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.447573094, -0.447573094}

Solution

x = {0, 7.447573094, -0.447573094}

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