14x^2+8x^3-5x^3-2x^2-5x^2-8x^4=

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Solution for 14x^2+8x^3-5x^3-2x^2-5x^2-8x^4= equation:


Simplifying
14x2 + 8x3 + -5x3 + -2x2 + -5x2 + -8x4 = 0

Reorder the terms:
14x2 + -2x2 + -5x2 + 8x3 + -5x3 + -8x4 = 0

Combine like terms: 14x2 + -2x2 = 12x2
12x2 + -5x2 + 8x3 + -5x3 + -8x4 = 0

Combine like terms: 12x2 + -5x2 = 7x2
7x2 + 8x3 + -5x3 + -8x4 = 0

Combine like terms: 8x3 + -5x3 = 3x3
7x2 + 3x3 + -8x4 = 0

Solving
7x2 + 3x3 + -8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(7 + 3x + -8x2) = 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 '(7 + 3x + -8x2)' equal to zero and attempt to solve: Simplifying 7 + 3x + -8x2 = 0 Solving 7 + 3x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.875 + -0.375x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -0.375x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -0.375x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -0.375x + x2 = 0 + 0.875 -0.375x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -0.375x + x2 = 0.875 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 0.875 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 0.875 + 0.03515625 Combine like terms: 0.875 + 0.03515625 = 0.91015625 0.03515625 + -0.375x + x2 = 0.91015625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 0.91015625 Calculate the square root of the right side: 0.954021095 Break this problem into two subproblems by setting (x + -0.1875) equal to 0.954021095 and -0.954021095.

Subproblem 1

x + -0.1875 = 0.954021095 Simplifying x + -0.1875 = 0.954021095 Reorder the terms: -0.1875 + x = 0.954021095 Solving -0.1875 + x = 0.954021095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.954021095 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.954021095 + 0.1875 x = 0.954021095 + 0.1875 Combine like terms: 0.954021095 + 0.1875 = 1.141521095 x = 1.141521095 Simplifying x = 1.141521095

Subproblem 2

x + -0.1875 = -0.954021095 Simplifying x + -0.1875 = -0.954021095 Reorder the terms: -0.1875 + x = -0.954021095 Solving -0.1875 + x = -0.954021095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.954021095 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.954021095 + 0.1875 x = -0.954021095 + 0.1875 Combine like terms: -0.954021095 + 0.1875 = -0.766521095 x = -0.766521095 Simplifying x = -0.766521095

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.141521095, -0.766521095}

Solution

x = {0, 1.141521095, -0.766521095}

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