SOLUTION: Step by step solving of the following equation: {{{ ((1/4)*x)+(2*sqrt(x))+15=x }}}

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Question 1087038: Step by step solving of the following equation:

Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website!
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There is nothing easier than it.

Introduce new variable y = . Then = x. Then your equation takes the form = ====> (Multiply both sides by 4) ====> = ====> = 0 ====> (apply the quadratic formula) ====> = = = . 1) = = = 6 ====> = = 36; 2) = = = ====> = = . Check each root. You will see that x = 36 is valid solution, while x = is EXTRANEOUS. Answer. The solution (and the only solution) is x = 36.

Illustration:

Plot y = (the left side of the original equation; red line) and y = x (the right side; green).

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!

Square

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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=50176 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 36, 11.1111111111111. Here's your graph:

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x = 36
x = 100/9 *** extraneous, not a solution