What is the answer to (4+sqrt(7+3p))/3 =8-p ?

The answer to (4+sqrt(7+3p))/3 =8-p is p=(41-sqrt(109))/6

Solve for p: (4+sqrt(7+3p))/3 =8-p

The solution is p=(41-sqrt(109))/6

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\frac{4 + 7 + 3 p}{3} = 8 - p

p = \frac{41 - 109}{6}

Decimal Notation

p = 5.09328 \dots

Solution steps

\frac{4 + 7 + 3 p}{3} = 8 - p

Multiply both sides by

3

\frac{4 + 7 + 3 p}{3} \cdot 3 = 8 \cdot 3 - p \cdot 3

Simplify

4 + 7 + 3 p = 24 - 3 p

Remove square roots

7 + 3 p = 9 p^{2} - 120 p + 400

Solve

7 + 3 p = 9 p^{2} - 120 p + 400 : p = \frac{41 + 109}{6}, p = \frac{41 - 109}{6}

p = \frac{41 + 109}{6}, p = \frac{41 - 109}{6}

Verify Solutions:

p = \frac{41 + 109}{6}

False

, p = \frac{41 - 109}{6}

True

The solution is

p = \frac{41 - 109}{6}

\frac{x + 5.5}{2} = 1.5

2 x + 3 - 7 = 0

(4 x - 1)^{\frac{5}{3}} = 32

(2 x + 7)^{\frac{1}{2}} = 5

500 (1 + 0.4 (x - 1)^{0.75}) = 48354

What is the answer to (4+sqrt(7+3p))/3 =8-p ?
The answer to (4+sqrt(7+3p))/3 =8-p is p=(41-sqrt(109))/6
Solve for p: (4+sqrt(7+3p))/3 =8-p
The solution is p=(41-sqrt(109))/6