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Question Solve for the value of jj that satisfies the equation (7j−9)(8j+9)=0(7j-9)(8j+9)=0.

Studdy Solution

STEP 1

Assumptions
1. We have a quadratic equation in the form of a product of two binomials set equal to zero.
2. We will use the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

STEP 2

Apply the Zero Product Property to the given equation.
(7j−9)(8j+9)=0 (7j - 9)(8j + 9) = 0

STEP 3

Set each factor equal to zero.
7j−9=0or8j+9=0 7j - 9 = 0 \quad \text{or} \quad 8j + 9 = 0

STEP 4

Solve the first equation for jj.
7j−9=0 7j - 9 = 0

STEP 5

Add 9 to both sides of the equation.
7j=9 7j = 9

STEP 6

Divide both sides by 7 to isolate jj.
j=97 j = \frac{9}{7}

STEP 7

Simplify the fraction.
j=97 j = \frac{9}{7}

STEP 8

Now solve the second equation for jj.
8j+9=0 8j + 9 = 0

STEP 9

Subtract 9 from both sides of the equation.
8j=−9 8j = -9

STEP 10

Divide both sides by 8 to isolate jj.
j=−98 j = \frac{-9}{8}

STEP 11

Simplify the fraction if possible.
j=−98 j = \frac{-9}{8}

STEP 12

Combine the solutions from both equations.
j=97orj=−98 j = \frac{9}{7} \quad \text{or} \quad j = \frac{-9}{8}
The solutions for jj are j=97j = \frac{9}{7} or j=−98j = \frac{-9}{8}.

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