-5x^20-7x^10+15=0

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Solution for -5x^20-7x^10+15=0 equation:


Simplifying
-5x20 + -7x10 + 15 = 0

Reorder the terms:
15 + -7x10 + -5x20 = 0

Solving
15 + -7x10 + -5x20 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-3 + 1.4x10 + x20 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 1.4x10 + 3 + x20 = 0 + 3

Reorder the terms:
-3 + 3 + 1.4x10 + x20 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 1.4x10 + x20 = 0 + 3
1.4x10 + x20 = 0 + 3

Combine like terms: 0 + 3 = 3
1.4x10 + x20 = 3

The x term is 1.4x10.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4x10 + 0.49 + x20 = 3 + 0.49

Reorder the terms:
0.49 + 1.4x10 + x20 = 3 + 0.49

Combine like terms: 3 + 0.49 = 3.49
0.49 + 1.4x10 + x20 = 3.49

Factor a perfect square on the left side:
(x10 + 0.7)(x10 + 0.7) = 3.49

Calculate the square root of the right side: 1.868154169

Break this problem into two subproblems by setting 
(x10 + 0.7) equal to 1.868154169 and -1.868154169.

Subproblem 1

x10 + 0.7 = 1.868154169 Simplifying x10 + 0.7 = 1.868154169 Reorder the terms: 0.7 + x10 = 1.868154169 Solving 0.7 + x10 = 1.868154169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x10 = 1.868154169 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x10 = 1.868154169 + -0.7 x10 = 1.868154169 + -0.7 Combine like terms: 1.868154169 + -0.7 = 1.168154169 x10 = 1.168154169 Simplifying x10 = 1.168154169 Reorder the terms: -1.168154169 + x10 = 1.168154169 + -1.168154169 Combine like terms: 1.168154169 + -1.168154169 = 0.000000000 -1.168154169 + x10 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2

x10 + 0.7 = -1.868154169 Simplifying x10 + 0.7 = -1.868154169 Reorder the terms: 0.7 + x10 = -1.868154169 Solving 0.7 + x10 = -1.868154169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x10 = -1.868154169 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x10 = -1.868154169 + -0.7 x10 = -1.868154169 + -0.7 Combine like terms: -1.868154169 + -0.7 = -2.568154169 x10 = -2.568154169 Simplifying x10 = -2.568154169 Reorder the terms: 2.568154169 + x10 = -2.568154169 + 2.568154169 Combine like terms: -2.568154169 + 2.568154169 = 0.000000000 2.568154169 + x10 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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