Math

Question Solve for the integer value(s) of nn in the equation 62=8n2+10-62=-8 n^{2}+10.

Studdy Solution

STEP 1

Assumptions
1. We are given the quadratic equation 62=8n2+10-62=-8n^2+10.
2. We need to solve for the variable nn.
3. The solution should be expressed as an integer or in simplest radical form.

STEP 2

First, we need to isolate the term containing n2n^2 by moving all other terms to the other side of the equation. We can do this by adding 8n28n^2 to both sides and subtracting 1010 from both sides.
62+8n210=8n2+8n2+1010-62 + 8n^2 - 10 = -8n^2 + 8n^2 + 10 - 10

STEP 3

Simplify the equation by combining like terms.
8n2=728n^2 = 72

STEP 4

Next, we need to solve for n2n^2 by dividing both sides of the equation by 88.
8n28=728\frac{8n^2}{8} = \frac{72}{8}

STEP 5

Calculate the value of n2n^2.
n2=9n^2 = 9

STEP 6

Now, we need to find the value of nn. Since n2=9n^2 = 9, we take the square root of both sides to solve for nn.
n=±9n = \pm\sqrt{9}

STEP 7

Calculate the square root of 99.
n=±3n = \pm3
The solutions for nn are n=3n = 3 and n=3n = -3.

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