Solve ((9x 7)/2)-x ((x-2)/7)=36

Question

Solve the equation

x_{1} = \frac{445 - 44 5 ^{2} - 4032}{4}, x_{2} = \frac{445 + 44 5 ^{2} - 4032}{4}

Alternative Form

x_{1} \approx 1.138409, x_{2} \approx 221.361591

Evaluate

((9 x \times 7) \div 2) - x ((x - 2) \div 7) = 36

Simplify

More Steps

\frac{63 x}{2} - \frac{x ( x - 2 )}{7} = 36

Multiply both sides of the equation by LCD

(\frac{63 x}{2} - \frac{x ( x - 2 )}{7}) \times 14 = 36 \times 14

Simplify the equation

More Steps

445 x - 2 x^{2} = 36 \times 14

Simplify the equation

445 x - 2 x^{2} = 504

Move the expression to the left side

445 x - 2 x^{2} - 504 = 0

Rewrite in standard form

- 2 x^{2} + 445 x - 504 = 0

Multiply both sides

2 x^{2} - 445 x + 504 = 0

Substitute a= 2,b= - 445 and c= 504 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{445 \pm ( - 445 ) ^{2} - 4 \times 2 \times 504}{2 \times 2}

Simplify the expression

x = \frac{445 \pm ( - 445 ) ^{2} - 4 \times 2 \times 504}{4}

Simplify the expression

More Steps

x = \frac{445 \pm 44 5 ^{2} - 4032}{4}

Separate the equation into 2 possible cases

x = \frac{445 + 44 5 ^{2} - 4032}{4} x = \frac{445 - 44 5 ^{2} - 4032}{4}

Solution

x_{1} = \frac{445 - 44 5 ^{2} - 4032}{4}, x_{2} = \frac{445 + 44 5 ^{2} - 4032}{4}

Alternative Form

x_{1} \approx 1.138409, x_{2} \approx 221.361591

Show Solution