Solve 16x^2=24x+1

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{3 - 10}{4}, x_{2} = \frac{3 + 10}{4}

Alternative Form

x_{1} \approx - 0.040569, x_{2} \approx 1.540569

Evaluate

16 x^{2} = 24 x + 1

Move the expression to the left side

16 x^{2} - 24 x - 1 = 0

Substitute a= 16,b= - 24 and c= - 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{24 \pm ( - 24 ) ^{2} - 4 \times 16 ( - 1 )}{2 \times 16}

Simplify the expression

x = \frac{24 \pm ( - 24 ) ^{2} - 4 \times 16 ( - 1 )}{32}

Simplify the expression

More Steps

x = \frac{24 \pm 640}{32}

Simplify the radical expression

More Steps

x = \frac{24 \pm 8 10}{32}

Separate the equation into 2 possible cases

x = \frac{24 + 8 10}{32} x = \frac{24 - 8 10}{32}

Simplify the expression

More Steps

x = \frac{3 + 10}{4} x = \frac{24 - 8 10}{32}

Simplify the expression

More Steps

x = \frac{3 + 10}{4} x = \frac{3 - 10}{4}

Solution

x_{1} = \frac{3 - 10}{4}, x_{2} = \frac{3 + 10}{4}

Alternative Form

x_{1} \approx - 0.040569, x_{2} \approx 1.540569

Show Solution