Solve x/6 x/3=18-x/4

Question

Solve the equation

x_{1} = - \frac{9 + 9 65}{4}, x_{2} = \frac{- 9 + 9 65}{4}

Alternative Form

x_{1} \approx - 20.39008, x_{2} \approx 15.89008

Evaluate

\frac{x}{6} \times \frac{x}{3} = 18 - \frac{x}{4}

Multiply the terms

More Steps

\frac{x ^{2}}{18} = 18 - \frac{x}{4}

Multiply both sides of the equation by LCD

\frac{x ^{2}}{18} \times 36 = (18 - \frac{x}{4}) \times 36

Simplify the equation

More Steps

2 x^{2} = (18 - \frac{x}{4}) \times 36

Simplify the equation

More Steps

2 x^{2} = 648 - 9 x

Move the expression to the left side

2 x^{2} - (648 - 9 x) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2 x^{2} - 648 + 9 x = 0

Rewrite in standard form

2 x^{2} + 9 x - 648 = 0

Substitute a= 2,b= 9 and c= - 648 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 9 \pm 9 ^{2} - 4 \times 2 ( - 648 )}{2 \times 2}

Simplify the expression

x = \frac{- 9 \pm 9 ^{2} - 4 \times 2 ( - 648 )}{4}

Simplify the expression

More Steps

x = \frac{- 9 \pm 5265}{4}

Simplify the radical expression

More Steps

x = \frac{- 9 \pm 9 65}{4}

Separate the equation into 2 possible cases

x = \frac{- 9 + 9 65}{4} x = \frac{- 9 - 9 65}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = \frac{- 9 + 9 65}{4} x = - \frac{9 + 9 65}{4}

Solution

x_{1} = - \frac{9 + 9 65}{4}, x_{2} = \frac{- 9 + 9 65}{4}

Alternative Form

x_{1} \approx - 20.39008, x_{2} \approx 15.89008

Show Solution

Solve the equation

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