Solve 4a^2=10-4a - ScanMath

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

a_{1} = - \frac{1 + 11}{2}, a_{2} = \frac{- 1 + 11}{2}

Alternative Form

a_{1} \approx - 2.158312, a_{2} \approx 1.158312

Evaluate

4 a^{2} = 10 - 4 a

Move the expression to the left side

4 a^{2} - 10 + 4 a = 0

Rewrite in standard form

4 a^{2} + 4 a - 10 = 0

Substitute a= 4,b= 4 and c= - 10 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{- 4 \pm 4 ^{2} - 4 \times 4 ( - 10 )}{2 \times 4}

Simplify the expression

a = \frac{- 4 \pm 4 ^{2} - 4 \times 4 ( - 10 )}{8}

Simplify the expression

More Steps

a = \frac{- 4 \pm 176}{8}

Simplify the radical expression

More Steps

a = \frac{- 4 \pm 4 11}{8}

Separate the equation into 2 possible cases

a = \frac{- 4 + 4 11}{8} a = \frac{- 4 - 4 11}{8}

Simplify the expression

More Steps

a = \frac{- 1 + 11}{2} a = \frac{- 4 - 4 11}{8}

Simplify the expression

More Steps

a = \frac{- 1 + 11}{2} a = - \frac{1 + 11}{2}

Solution

a_{1} = - \frac{1 + 11}{2}, a_{2} = \frac{- 1 + 11}{2}

Alternative Form

a_{1} \approx - 2.158312, a_{2} \approx 1.158312

Show Solution