Solve for x
x=-\sqrt{5}\approx -2.236067977
x=\sqrt{5}\approx 2.236067977
x=1
x=-1
Graph
Share
Copied to clipboard
t^{2}-6t+5=0
Substitute t for x^{2}.
t=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 1\times 5}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -6 for b, and 5 for c in the quadratic formula.
t=\frac{6±4}{2}
Do the calculations.
t=5 t=1
Solve the equation t=\frac{6±4}{2} when ± is plus and when ± is minus.
x=\sqrt{5} x=-\sqrt{5} x=1 x=-1
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}