(6x^3-7x)+(5x^2+4x)=

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Solution for (6x^3-7x)+(5x^2+4x)= equation:


Simplifying
(6x3 + -7x) + (5x2 + 4x) = 0

Reorder the terms:
(-7x + 6x3) + (5x2 + 4x) = 0

Remove parenthesis around (-7x + 6x3)
-7x + 6x3 + (5x2 + 4x) = 0

Reorder the terms:
-7x + 6x3 + (4x + 5x2) = 0

Remove parenthesis around (4x + 5x2)
-7x + 6x3 + 4x + 5x2 = 0

Reorder the terms:
-7x + 4x + 5x2 + 6x3 = 0

Combine like terms: -7x + 4x = -3x
-3x + 5x2 + 6x3 = 0

Solving
-3x + 5x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + 5x + 6x2) = 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 '(-3 + 5x + 6x2)' equal to zero and attempt to solve: Simplifying -3 + 5x + 6x2 = 0 Solving -3 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.8333333333x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.8333333333x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.8333333333x + x2 = 0 + 0.5 0.8333333333x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.8333333333x + x2 = 0.5 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 0.5 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 0.5 + 0.1736111111 Combine like terms: 0.5 + 0.1736111111 = 0.6736111111 0.1736111111 + 0.8333333333x + x2 = 0.6736111111 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 0.6736111111 Calculate the square root of the right side: 0.82073815 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 0.82073815 and -0.82073815.

Subproblem 1

x + 0.4166666667 = 0.82073815 Simplifying x + 0.4166666667 = 0.82073815 Reorder the terms: 0.4166666667 + x = 0.82073815 Solving 0.4166666667 + x = 0.82073815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 0.82073815 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 0.82073815 + -0.4166666667 x = 0.82073815 + -0.4166666667 Combine like terms: 0.82073815 + -0.4166666667 = 0.4040714833 x = 0.4040714833 Simplifying x = 0.4040714833

Subproblem 2

x + 0.4166666667 = -0.82073815 Simplifying x + 0.4166666667 = -0.82073815 Reorder the terms: 0.4166666667 + x = -0.82073815 Solving 0.4166666667 + x = -0.82073815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -0.82073815 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -0.82073815 + -0.4166666667 x = -0.82073815 + -0.4166666667 Combine like terms: -0.82073815 + -0.4166666667 = -1.2374048167 x = -1.2374048167 Simplifying x = -1.2374048167

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4040714833, -1.2374048167}

Solution

x = {0, 0.4040714833, -1.2374048167}

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