Solve {left(3/2right)}^2+33/2=2

$${ \left( \frac{ 3 }{ 2 } \right) }^{ 2 } +3 \frac{ 3 }{ 2 } = 2$$

Verify

Solution Steps

Multiply both sides of the equation by 2.

$$2\times \left(\frac{3}{2}\right)^{2}+3\times 2+3=4$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$2\times \frac{9}{4}+3\times 2+3=4$$

Express 2\times \frac{9}{4} as a single fraction.

$$\frac{2\times 9}{4}+3\times 2+3=4$$

Multiply 2 and 9 to get 18.

$$\frac{18}{4}+3\times 2+3=4$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{9}{2}+3\times 2+3=4$$

Multiply 3 and 2 to get 6.

$$\frac{9}{2}+6+3=4$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{9}{2}+\frac{12}{2}+3=4$$

Since \frac{9}{2} and \frac{12}{2} have the same denominator, add them by adding their numerators.

$$\frac{9+12}{2}+3=4$$

Add 9 and 12 to get 21.

$$\frac{21}{2}+3=4$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{21}{2}+\frac{6}{2}=4$$

Since \frac{21}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{21+6}{2}=4$$

Add 21 and 6 to get 27.

$$\frac{27}{2}=4$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{27}{2}=\frac{8}{2}$$

Compare \frac{27}{2} and \frac{8}{2}.

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