Solve 1/2 x^(2)=7x-1

Evaluate

\frac{1}{2} x^{2} = 7 x - 1

Move the expression to the left side

\frac{1}{2} x^{2} - 7 x + 1 = 0

Multiply both sides

2 (\frac{1}{2} x^{2} - 7 x + 1) = 2 \times 0

Calculate

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

Substitute a= 1,b= - 14 and c= 2 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

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

Simplify the expression

More Steps

x = \frac{14 \pm 188}{2}

Simplify the radical expression

More Steps

x = \frac{14 \pm 2 47}{2}

Separate the equation into 2 possible cases

x = \frac{14 + 2 47}{2} x = \frac{14 - 2 47}{2}

Simplify the expression

More Steps

x = 7 + 47 x = \frac{14 - 2 47}{2}

Simplify the expression

More Steps

x = 7 + 47 x = 7 - 47

Solution

x_{1} = 7 - 47, x_{2} = 7 + 47

Alternative Form

x_{1} \approx 0.144345, x_{2} \approx 13.855655

Solve the quadratic equation