Math / Algebra

Question $y+\frac{6}{y}=-7$

Studdy Solution

STEP 1

1. The equation $y + \frac{6}{y} = -7$ is a rational equation.
2. We will need to eliminate the fraction to solve for $y$ .

STEP 2

1. Eliminate the fraction by multiplying through by $y$ .
2. Rearrange the equation to form a quadratic equation.
3. Solve the quadratic equation for $y$ .

STEP 3

Multiply every term in the equation by $y$ to eliminate the fraction:
$y \cdot y + y \cdot \frac{6}{y} = -7 \cdot y$
This simplifies to:
$y^2 + 6 = -7y$

STEP 4

Rearrange the equation to bring all terms to one side, forming a quadratic equation:
$y^2 + 7y + 6 = 0$

STEP 5

Solve the quadratic equation using the quadratic formula, factoring, or completing the square. Here, we will factor:
The equation $y^2 + 7y + 6 = 0$ can be factored as:
$(y + 6)(y + 1) = 0$

STEP 6

Set each factor equal to zero and solve for $y$ :
1. $y + 6 = 0$ gives $y = -6$
2. $y + 1 = 0$ gives $y = -1$
The solutions for $y$ are:
$y = -6 \quad \text{or} \quad y = -1$

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Question $y+\frac{6}{y}=-7$

Studdy Solution

STEP 1

1. The equation $y + \frac{6}{y} = -7$ is a rational equation.
2. We will need to eliminate the fraction to solve for $y$ .

STEP 2

1. Eliminate the fraction by multiplying through by $y$ .
2. Rearrange the equation to form a quadratic equation.
3. Solve the quadratic equation for $y$ .

STEP 3

Multiply every term in the equation by $y$ to eliminate the fraction:
$y \cdot y + y \cdot \frac{6}{y} = -7 \cdot y$
This simplifies to:
$y^2 + 6 = -7y$

STEP 4

Rearrange the equation to bring all terms to one side, forming a quadratic equation:
$y^2 + 7y + 6 = 0$

STEP 5

Solve the quadratic equation using the quadratic formula, factoring, or completing the square. Here, we will factor:
The equation $y^2 + 7y + 6 = 0$ can be factored as:
$(y + 6)(y + 1) = 0$

STEP 6

Set each factor equal to zero and solve for $y$ :
1. $y + 6 = 0$ gives $y = -6$
2. $y + 1 = 0$ gives $y = -1$
The solutions for $y$ are:
$y = -6 \quad \text{or} \quad y = -1$

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Questiony+6y=−7y+\frac{6}{y}=-7y+y6​=−7

Studdy Solution

STEP 1

1. The equation y+6y=−7 y + \frac{6}{y} = -7 y+y6​=−7 is a rational equation.2. We will need to eliminate the fraction to solve for y y y.

STEP 2

1. Eliminate the fraction by multiplying through by y y y.2. Rearrange the equation to form a quadratic equation.3. Solve the quadratic equation for y y y.

STEP 3

Multiply every term in the equation by y y y to eliminate the fraction:y⋅y+y⋅6y=−7⋅y y \cdot y + y \cdot \frac{6}{y} = -7 \cdot y y⋅y+y⋅y6​=−7⋅yThis simplifies to:y2+6=−7y y^2 + 6 = -7y y2+6=−7y

STEP 4

Rearrange the equation to bring all terms to one side, forming a quadratic equation:y2+7y+6=0 y^2 + 7y + 6 = 0 y2+7y+6=0

STEP 5

Solve the quadratic equation using the quadratic formula, factoring, or completing the square. Here, we will factor:The equation y2+7y+6=0 y^2 + 7y + 6 = 0 y2+7y+6=0 can be factored as:(y+6)(y+1)=0 (y + 6)(y + 1) = 0 (y+6)(y+1)=0

STEP 6

Set each factor equal to zero and solve for y y y:1. y+6=0 y + 6 = 0 y+6=0 gives y=−6 y = -6 y=−62. y+1=0 y + 1 = 0 y+1=0 gives y=−1 y = -1 y=−1 The solutions for y y y are:y=−6ory=−1 y = -6 \quad \text{or} \quad y = -1 y=−6ory=−1

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Studdy solves anything!

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Question $y+\frac{6}{y}=-7$

1. The equation $y + \frac{6}{y} = -7$ is a rational equation.
2. We will need to eliminate the fraction to solve for $y$ .

1. Eliminate the fraction by multiplying through by $y$ .
2. Rearrange the equation to form a quadratic equation.
3. Solve the quadratic equation for $y$ .

Multiply every term in the equation by $y$ to eliminate the fraction:
$y \cdot y + y \cdot \frac{6}{y} = -7 \cdot y$
This simplifies to:
$y^2 + 6 = -7y$

Rearrange the equation to bring all terms to one side, forming a quadratic equation:
$y^2 + 7y + 6 = 0$

Solve the quadratic equation using the quadratic formula, factoring, or completing the square. Here, we will factor:
The equation $y^2 + 7y + 6 = 0$ can be factored as:
$(y + 6)(y + 1) = 0$

Set each factor equal to zero and solve for $y$ :
1. $y + 6 = 0$ gives $y = -6$
2. $y + 1 = 0$ gives $y = -1$
The solutions for $y$ are:
$y = -6 \quad \text{or} \quad y = -1$