Solve x^2-7x^49/4=89/4

Evaluate

x^{2} - 7 x^{4} \times \frac{9}{4} = \frac{89}{4}

Multiply the terms

More Steps

x^{2} - \frac{63}{4} x^{4} = \frac{89}{4}

Move the expression to the left side

x^{2} - \frac{63}{4} x^{4} - \frac{89}{4} = 0

Solve the equation using substitution t = x^{2}

t - \frac{63}{4} t^{2} - \frac{89}{4} = 0

Rewrite in standard form

- \frac{63}{4} t^{2} + t - \frac{89}{4} = 0

Multiply both sides

\frac{63}{4} t^{2} - t + \frac{89}{4} = 0

Multiply both sides

4 (\frac{63}{4} t^{2} - t + \frac{89}{4}) = 4 \times 0

Calculate

63 t^{2} - 4 t + 89 = 0

Substitute a= 63,b= - 4 and c= 89 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 63 \times 89}{2 \times 63}

Simplify the expression

t = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 63 \times 89}{126}

Simplify the expression

More Steps

t = \frac{4 \pm - 22412}{126}

The expression is undefined in the set of real numbers

t \in / R

Solution

x \in / R

Alternative Form

No real solution

Solve the equation