Basic Math Examples

$65^{2} = {(A + (5.5 \cos (270)))}^{2}$

Step 1

Rewrite the equation as ${(A + 5.5 \cos (270))}^{2} = 65^{2}$ .

${(A + 5.5 \cos (270))}^{2} = 65^{2}$

Step 2

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$| A + 5.5 \cos (270) | = | 65 |$

Step 3

Solve for $A$ .

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Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$A + 5.5 \cos (270) = \pm | 65 |$

The absolute value is the distance between a number and zero. The distance between $0$ and $65$ is $65$ .

$A + 5.5 \cos (270) = \pm 65$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the first solution.

$A + 5.5 \cos (270) = 65$

Simplify $A + 5.5 \cos (270)$ .

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Simplify each term.

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Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

$A + 5.5 (- \cos (90)) = 65$

The exact value of $\cos (90)$ is $0$ .

$A + 5.5 (- 0) = 65$

Multiply $5.5 (- 0)$ .

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Multiply $- 1$ by $0$ .

$A + 5.5 \cdot 0 = 65$

Multiply $5.5$ by $0$ .

$A + 0 = 65$

Add $A$ and $0$ .

$A = 65$

Next, use the negative value of the $\pm$ to find the second solution.

$A + 5.5 \cos (270) = - 65$

Simplify $A + 5.5 \cos (270)$ .

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Simplify each term.

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Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

$A + 5.5 (- \cos (90)) = - 65$

The exact value of $\cos (90)$ is $0$ .

$A + 5.5 (- 0) = - 65$

Multiply $5.5 (- 0)$ .

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Multiply $- 1$ by $0$ .

$A + 5.5 \cdot 0 = - 65$

Multiply $5.5$ by $0$ .

$A + 0 = - 65$

Add $A$ and $0$ .

$A = - 65$

The complete solution is the result of both the positive and negative portions of the solution.

$A = 65, - 65$