Solve x-22/x-32 - ScanMath

Question

Simplify the expression

\frac{x ^{2} - 22 - 32 x}{x}

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x = 0

Show Solution

x_{1} = 16 - 278, x_{2} = 16 + 278

Alternative Form

x_{1} \approx - 0.673332, x_{2} \approx 32.673332

Evaluate

x - \frac{22}{x} - 32

To find the roots of the expression,set the expression equal to 0

x - \frac{22}{x} - 32 = 0

Find the domain

x - \frac{22}{x} - 32 = 0, x \neq = 0

Calculate

x - \frac{22}{x} - 32 = 0

Subtract the terms

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\frac{x ^{2} - 22}{x} - 32 = 0

Subtract the terms

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\frac{x ^{2} - 22 - 32 x}{x} = 0

Cross multiply

x^{2} - 22 - 32 x = x \times 0

Simplify the equation

x^{2} - 22 - 32 x = 0

Rewrite in standard form

x^{2} - 32 x - 22 = 0

Substitute a= 1,b= - 32 and c= - 22 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{32 \pm ( - 32 ) ^{2} - 4 ( - 22 )}{2}

Simplify the expression

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x = \frac{32 \pm 1112}{2}

Simplify the radical expression

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x = \frac{32 \pm 2 278}{2}

Separate the equation into 2 possible cases

x = \frac{32 + 2 278}{2} x = \frac{32 - 2 278}{2}

Simplify the expression

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x = 16 + 278 x = \frac{32 - 2 278}{2}

Simplify the expression

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x = 16 + 278 x = 16 - 278

Check if the solution is in the defined range

x = 16 + 278 x = 16 - 278, x \neq = 0

Find the intersection of the solution and the defined range

x = 16 + 278 x = 16 - 278

Solution

x_{1} = 16 - 278, x_{2} = 16 + 278

Alternative Form

x_{1} \approx - 0.673332, x_{2} \approx 32.673332

Show Solution