QuestionSolve for $x$ : $x + \frac{6}{x} = 5$ .

Studdy Solution

STEP 1

Assumptions1. The equation to be solved is $x+\frac{6}{x}=5$ . We are looking for the value(s) of $x$ that satisfy the equation

STEP 2

The given equation is a rational equation, which means it involves a fraction. To make it easier to solve, we can eliminate the fraction by multiplying every term by $x$ .
$x(x) + \frac{6}{x}(x) =5(x)$

STEP 3

implify the equation.
$x^2 +6 =5x$

STEP 4

Rearrange the equation to set it equal to zero. This is because we can solve for $x$ by factoring or using the quadratic formula, but the equation must be in the form $ax^2 + bx + c =0$ .
$x^2 -x +6 =0$

STEP 5

Now, we can factor the quadratic equation. We are looking for two numbers that multiply to $$ and add to $-5$.
$(x -2)(x -3) =0$

STEP 6

Set each factor equal to zero and solve for $x$ .
$x -2 =0 \quad \text{and} \quad x -3 =0$

STEP 7

olving the above equations gives the solutions.
$x =2 \quad \text{and} \quad x =3$ These are the solutions to the equation $x+\frac{6}{x}=5$ .

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QuestionSolve for $x$ : $x + \frac{6}{x} = 5$ .

Studdy Solution

STEP 1

Assumptions1. The equation to be solved is $x+\frac{6}{x}=5$ . We are looking for the value(s) of $x$ that satisfy the equation

STEP 2

The given equation is a rational equation, which means it involves a fraction. To make it easier to solve, we can eliminate the fraction by multiplying every term by $x$ .
$x(x) + \frac{6}{x}(x) =5(x)$

STEP 3

implify the equation.
$x^2 +6 =5x$

STEP 4

Rearrange the equation to set it equal to zero. This is because we can solve for $x$ by factoring or using the quadratic formula, but the equation must be in the form $ax^2 + bx + c =0$ .
$x^2 -x +6 =0$

STEP 5

Now, we can factor the quadratic equation. We are looking for two numbers that multiply to $$ and add to $-5$.
$(x -2)(x -3) =0$

STEP 6

Set each factor equal to zero and solve for $x$ .
$x -2 =0 \quad \text{and} \quad x -3 =0$

STEP 7

olving the above equations gives the solutions.
$x =2 \quad \text{and} \quad x =3$ These are the solutions to the equation $x+\frac{6}{x}=5$ .

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QuestionSolve for xxx: x+6x=5x + \frac{6}{x} = 5x+x6​=5.

Studdy Solution

STEP 1

Assumptions1. The equation to be solved is x+6x=5x+\frac{6}{x}=5x+x6​=5 . We are looking for the value(s) of xxx that satisfy the equation

STEP 2

The given equation is a rational equation, which means it involves a fraction. To make it easier to solve, we can eliminate the fraction by multiplying every term by xxx.x(x)+6x(x)=5(x)x(x) + \frac{6}{x}(x) =5(x)x(x)+x6​(x)=5(x)

STEP 3

implify the equation.x2+6=5xx^2 +6 =5xx2+6=5x

STEP 4

Rearrange the equation to set it equal to zero. This is because we can solve for xxx by factoring or using the quadratic formula, but the equation must be in the form ax2+bx+c=0ax^2 + bx + c =0ax2+bx+c=0.x2−x+6=0x^2 -x +6 =0x2−x+6=0

STEP 5

Now, we can factor the quadratic equation. We are looking for two numbers that multiply to $$ and add to $-5$.(x−2)(x−3)=0(x -2)(x -3) =0(x−2)(x−3)=0

STEP 6

Set each factor equal to zero and solve for xxx.x−2=0andx−3=0x -2 =0 \quad \text{and} \quad x -3 =0x−2=0andx−3=0

STEP 7

olving the above equations gives the solutions.x=2andx=3x =2 \quad \text{and} \quad x =3x=2andx=3These are the solutions to the equation x+6x=5x+\frac{6}{x}=5x+x6​=5.

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QuestionSolve for $x$ : $x + \frac{6}{x} = 5$ .

Assumptions1. The equation to be solved is $x+\frac{6}{x}=5$ . We are looking for the value(s) of $x$ that satisfy the equation

The given equation is a rational equation, which means it involves a fraction. To make it easier to solve, we can eliminate the fraction by multiplying every term by $x$ .
$x(x) + \frac{6}{x}(x) =5(x)$

implify the equation.
$x^2 +6 =5x$

Rearrange the equation to set it equal to zero. This is because we can solve for $x$ by factoring or using the quadratic formula, but the equation must be in the form $ax^2 + bx + c =0$ .
$x^2 -x +6 =0$

Now, we can factor the quadratic equation. We are looking for two numbers that multiply to $$ and add to $-5$.
$(x -2)(x -3) =0$

Set each factor equal to zero and solve for $x$ .
$x -2 =0 \quad \text{and} \quad x -3 =0$

olving the above equations gives the solutions.
$x =2 \quad \text{and} \quad x =3$ These are the solutions to the equation $x+\frac{6}{x}=5$ .