9x^3(-5x^4+9x^3+7x^2)=0

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Solution for 9x^3(-5x^4+9x^3+7x^2)=0 equation:


Simplifying
9x3(-5x4 + 9x3 + 7x2) = 0

Reorder the terms:
9x3(7x2 + 9x3 + -5x4) = 0
(7x2 * 9x3 + 9x3 * 9x3 + -5x4 * 9x3) = 0
(63x5 + 81x6 + -45x7) = 0

Solving
63x5 + 81x6 + -45x7 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x5'.
9x5(7 + 9x + -5x2) = 0

Ignore the factor 9.

Subproblem 1

Set the factor 'x5' equal to zero and attempt to solve: Simplifying x5 = 0 Solving x5 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x5 = 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 '(7 + 9x + -5x2)' equal to zero and attempt to solve: Simplifying 7 + 9x + -5x2 = 0 Solving 7 + 9x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.4 + -1.8x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -1.8x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -1.8x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -1.8x + x2 = 0 + 1.4 -1.8x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -1.8x + x2 = 1.4 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 1.4 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 1.4 + 0.81 Combine like terms: 1.4 + 0.81 = 2.21 0.81 + -1.8x + x2 = 2.21 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 2.21 Calculate the square root of the right side: 1.486606875 Break this problem into two subproblems by setting (x + -0.9) equal to 1.486606875 and -1.486606875.

Subproblem 1

x + -0.9 = 1.486606875 Simplifying x + -0.9 = 1.486606875 Reorder the terms: -0.9 + x = 1.486606875 Solving -0.9 + x = 1.486606875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 1.486606875 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 1.486606875 + 0.9 x = 1.486606875 + 0.9 Combine like terms: 1.486606875 + 0.9 = 2.386606875 x = 2.386606875 Simplifying x = 2.386606875

Subproblem 2

x + -0.9 = -1.486606875 Simplifying x + -0.9 = -1.486606875 Reorder the terms: -0.9 + x = -1.486606875 Solving -0.9 + x = -1.486606875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -1.486606875 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -1.486606875 + 0.9 x = -1.486606875 + 0.9 Combine like terms: -1.486606875 + 0.9 = -0.586606875 x = -0.586606875 Simplifying x = -0.586606875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.386606875, -0.586606875}

Solution

x = {2.386606875, -0.586606875}

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