6x^8-48x^7+30x^6=0

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Solution for 6x^8-48x^7+30x^6=0 equation:


Simplifying
6x8 + -48x7 + 30x6 = 0

Reorder the terms:
30x6 + -48x7 + 6x8 = 0

Solving
30x6 + -48x7 + 6x8 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x6'.
6x6(5 + -8x + x2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor 'x6' equal to zero and attempt to solve: Simplifying x6 = 0 Solving x6 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x6 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(5 + -8x + x2)' equal to zero and attempt to solve: Simplifying 5 + -8x + x2 = 0 Solving 5 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -8x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -8x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8x + x2 = 0 + -5 -8x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -8x + x2 = -5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -5 + 16 Reorder the terms: 16 + -8x + x2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + -8x + x2 = 11 Factor a perfect square on the left side: (x + -4)(x + -4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -4) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + -4 = 3.31662479 Simplifying x + -4 = 3.31662479 Reorder the terms: -4 + x = 3.31662479 Solving -4 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.31662479 + 4 x = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 x = 7.31662479 Simplifying x = 7.31662479

Subproblem 2

x + -4 = -3.31662479 Simplifying x + -4 = -3.31662479 Reorder the terms: -4 + x = -3.31662479 Solving -4 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.31662479 + 4 x = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 x = 0.68337521 Simplifying x = 0.68337521

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.31662479, 0.68337521}

Solution

x = {7.31662479, 0.68337521}

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