4x^3+7x^2-5x=0

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


Simplifying
4x3 + 7x2 + -5x = 0

Reorder the terms:
-5x + 7x2 + 4x3 = 0

Solving
-5x + 7x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 7x + 4x2) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(-5 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + 7x + 4x2 = 0 Solving -5 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 1.75x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.75x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.75x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.75x + x2 = 0 + 1.25 1.75x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.75x + x2 = 1.25 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 1.25 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 1.25 + 0.765625 Combine like terms: 1.25 + 0.765625 = 2.015625 0.765625 + 1.75x + x2 = 2.015625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (x + 0.875) equal to 1.419727086 and -1.419727086.

Subproblem 1

x + 0.875 = 1.419727086 Simplifying x + 0.875 = 1.419727086 Reorder the terms: 0.875 + x = 1.419727086 Solving 0.875 + x = 1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.419727086 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.419727086 + -0.875 x = 1.419727086 + -0.875 Combine like terms: 1.419727086 + -0.875 = 0.544727086 x = 0.544727086 Simplifying x = 0.544727086

Subproblem 2

x + 0.875 = -1.419727086 Simplifying x + 0.875 = -1.419727086 Reorder the terms: 0.875 + x = -1.419727086 Solving 0.875 + x = -1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.419727086 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.419727086 + -0.875 x = -1.419727086 + -0.875 Combine like terms: -1.419727086 + -0.875 = -2.294727086 x = -2.294727086 Simplifying x = -2.294727086

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.544727086, -2.294727086}

Solution

x = {0, 0.544727086, -2.294727086}

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