10x^3+14x^2-16x=

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Solution for 10x^3+14x^2-16x= equation:


Simplifying
10x3 + 14x2 + -16x = 0

Reorder the terms:
-16x + 14x2 + 10x3 = 0

Solving
-16x + 14x2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-8 + 7x + 5x2) = 0

Ignore the factor 2.

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 '(-8 + 7x + 5x2)' equal to zero and attempt to solve: Simplifying -8 + 7x + 5x2 = 0 Solving -8 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 1.4x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 1.4x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 1.4x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 1.4x + x2 = 0 + 1.6 1.4x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 1.4x + x2 = 1.6 The x term is 1.4x. 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. 1.4x + 0.49 + x2 = 1.6 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 1.6 + 0.49 Combine like terms: 1.6 + 0.49 = 2.09 0.49 + 1.4x + x2 = 2.09 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (x + 0.7) equal to 1.445683229 and -1.445683229.

Subproblem 1

x + 0.7 = 1.445683229 Simplifying x + 0.7 = 1.445683229 Reorder the terms: 0.7 + x = 1.445683229 Solving 0.7 + x = 1.445683229 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 + x = 1.445683229 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 1.445683229 + -0.7 x = 1.445683229 + -0.7 Combine like terms: 1.445683229 + -0.7 = 0.745683229 x = 0.745683229 Simplifying x = 0.745683229

Subproblem 2

x + 0.7 = -1.445683229 Simplifying x + 0.7 = -1.445683229 Reorder the terms: 0.7 + x = -1.445683229 Solving 0.7 + x = -1.445683229 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 + x = -1.445683229 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -1.445683229 + -0.7 x = -1.445683229 + -0.7 Combine like terms: -1.445683229 + -0.7 = -2.145683229 x = -2.145683229 Simplifying x = -2.145683229

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.745683229, -2.145683229}

Solution

x = {0, 0.745683229, -2.145683229}

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