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

Question

Solve the equation

x_{1} = \frac{91 - 4249}{28}, x_{2} = \frac{91 + 4249}{28}

Alternative Form

x_{1} \approx 0.921987, x_{2} \approx 5.578013

Evaluate

(\frac{9 x \times 7}{2}) - x ((x - 2) \times 7) = 36

Remove the parentheses

(\frac{9 x \times 7}{2}) - x (x - 2) \times 7 = 36

Simplify

More Steps

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

Multiply both sides of the equation by LCD

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

Simplify the equation

More Steps

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

Simplify the equation

91 x - 14 x^{2} = 72

Move the expression to the left side

91 x - 14 x^{2} - 72 = 0

Rewrite in standard form

- 14 x^{2} + 91 x - 72 = 0

Multiply both sides

14 x^{2} - 91 x + 72 = 0

Substitute a= 14,b= - 91 and c= 72 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{91 \pm ( - 91 ) ^{2} - 4 \times 14 \times 72}{2 \times 14}

Simplify the expression

x = \frac{91 \pm ( - 91 ) ^{2} - 4 \times 14 \times 72}{28}

Simplify the expression

More Steps

x = \frac{91 \pm 4249}{28}

Separate the equation into 2 possible cases

x = \frac{91 + 4249}{28} x = \frac{91 - 4249}{28}

Solution

x_{1} = \frac{91 - 4249}{28}, x_{2} = \frac{91 + 4249}{28}

Alternative Form

x_{1} \approx 0.921987, x_{2} \approx 5.578013

Show Solution