Solve for x

A. 1/x(6x^3+5x^2)=21
B. X/2+6=-10/x
C. X+6=[x+12]^2

#1

multiply both sides by x
6x^3 + 5x^2 = 21x
x(6x^2+ 5x - 21) = 0
x=0
or
x= -5±√529)/12
= (-5 ± 23)/12 = 3/2 or -7/3

but x ≠ 0 in the original equation, we can't divide by zero

x = 3/2 or x = -7/3

B) multiply each term by 2x
x^2 + 12x = -20
x^2 + 12x + 20 = 0
(x+10(x+2) = 0
x = -10 or x = -2

C) expand it first
x+6 = x^2 + 24x + 144
take over ....

thanks reiny I got all of those correct thanks alot

Sure, I can help you solve these equations. Let's go through each one step by step.

A. 1/x(6x^3+5x^2)=21

To solve this equation, we need to eliminate the fraction first. We can do this by multiplying both sides of the equation by x:

1 * (6x^3 + 5x^2) = 21 * x

Now we distribute the x on the left side:

6x^3 + 5x^2 = 21x

Next, we rearrange the equation to set it equal to zero:

6x^3 + 5x^2 - 21x = 0

Now we have a cubic equation. Unfortunately, there is no simple algebraic method for solving it, so we'll need to use numerical or graphical methods to approximate the solutions. One such method is the Newton-Raphson method.

B. x/2 + 6 = -10/x

To solve this equation, we start by multiplying both sides of the equation by x to eliminate the fraction:

x * (x/2 + 6) = x * (-10/x)

Now we distribute the x on the left side:

x^2/2 + 6x = -10

Rearrange the equation to set it equal to zero:

x^2/2 + 6x + 10 = 0

This is a quadratic equation. We can solve it either by factoring, completing the square, or by using the quadratic formula. Let's use the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac))/(2a)

In our case, a = 1/2, b = 6, and c = 10. Plugging these values into the quadratic formula, we get:

x = (-6 ± √(6^2 - 4 * (1/2) * 10))/(2 * (1/2))

Simplifying this expression gives us the two solutions for x.

C. x + 6 = (x + 12)^2

Expanding the right side using the formula (a + b)^2 = a^2 + 2ab + b^2, we get:

x + 6 = x^2 + 24x + 144

Rearrange the equation to set it equal to zero:

x^2 + 24x + 144 - x - 6 = 0

Combine like terms:

x^2 + 23x + 138 = 0

This is a quadratic equation. We can solve it by factoring, completing the square, or by using the quadratic formula.