Solve 2y (7y - 4) = 41

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

y_{1} = \frac{4 - 590}{14}, y_{2} = \frac{4 + 590}{14}

Alternative Form

y_{1} \approx - 1.44928, y_{2} \approx 2.020708

Evaluate

2 y (7 y - 4) = 41

Expand the expression

More Steps

14 y^{2} - 8 y = 41

Move the expression to the left side

14 y^{2} - 8 y - 41 = 0

Substitute a= 14,b= - 8 and c= - 41 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 14 ( - 41 )}{2 \times 14}

Simplify the expression

y = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 14 ( - 41 )}{28}

Simplify the expression

More Steps

y = \frac{8 \pm 2360}{28}

Simplify the radical expression

More Steps

y = \frac{8 \pm 2 590}{28}

Separate the equation into 2 possible cases

y = \frac{8 + 2 590}{28} y = \frac{8 - 2 590}{28}

Simplify the expression

More Steps

y = \frac{4 + 590}{14} y = \frac{8 - 2 590}{28}

Simplify the expression

More Steps

y = \frac{4 + 590}{14} y = \frac{4 - 590}{14}

Solution

y_{1} = \frac{4 - 590}{14}, y_{2} = \frac{4 + 590}{14}

Alternative Form

y_{1} \approx - 1.44928, y_{2} \approx 2.020708

Show Solution