Solve 4x= (-3)/2 -(-x 1) 5/4 x

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{8 - 94}{5}, x_{2} = \frac{8 + 94}{5}

Alternative Form

x_{1} \approx - 0.339072, x_{2} \approx 3.539072

Evaluate

4 x = \frac{- 3}{2} - (- x \times 1) \times \frac{5}{4} x

Calculate

4 x = \frac{- 3}{2} - (- x \times 1 \times \frac{5}{4} x)

Simplify

More Steps

4 x = - \frac{3}{2} + \frac{5}{4} x^{2}

Swap the sides

- \frac{3}{2} + \frac{5}{4} x^{2} = 4 x

Move the expression to the left side

- \frac{3}{2} + \frac{5}{4} x^{2} - 4 x = 0

Rewrite in standard form

\frac{5}{4} x^{2} - 4 x - \frac{3}{2} = 0

Multiply both sides

4 (\frac{5}{4} x^{2} - 4 x - \frac{3}{2}) = 4 \times 0

Calculate

5 x^{2} - 16 x - 6 = 0

Substitute a= 5,b= - 16 and c= - 6 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{16 \pm ( - 16 ) ^{2} - 4 \times 5 ( - 6 )}{2 \times 5}

Simplify the expression

x = \frac{16 \pm ( - 16 ) ^{2} - 4 \times 5 ( - 6 )}{10}

Simplify the expression

More Steps

x = \frac{16 \pm 376}{10}

Simplify the radical expression

More Steps

x = \frac{16 \pm 2 94}{10}

Separate the equation into 2 possible cases

x = \frac{16 + 2 94}{10} x = \frac{16 - 2 94}{10}

Simplify the expression

More Steps

x = \frac{8 + 94}{5} x = \frac{16 - 2 94}{10}

Simplify the expression

More Steps

x = \frac{8 + 94}{5} x = \frac{8 - 94}{5}

Solution

x_{1} = \frac{8 - 94}{5}, x_{2} = \frac{8 + 94}{5}

Alternative Form

x_{1} \approx - 0.339072, x_{2} \approx 3.539072

Show Solution