Solve for x

x=\sqrt{y-1}<br/>x=-\sqrt{y-1}\text{, }y\geq 1

$x=y−1 $

$x=−y−1 ,y≥1$

$x=−y−1 ,y≥1$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Solve for x (complex solution)

x=-\sqrt{y-1}<br/>x=\sqrt{y-1}

$x=−y−1 $

$x=y−1 $

$x=y−1 $

Solve for y

y=x^{2}+1

$y=x_{2}+1$

Assign y

y≔x^{2}+1

$y:=x_{2}+1$

Graph

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x^{2}+1=y

Swap sides so that all variable terms are on the left hand side.

x^{2}=y-1

Subtract 1 from both sides.

x=\sqrt{y-1} x=-\sqrt{y-1}

Take the square root of both sides of the equation.

x^{2}+1=y

Swap sides so that all variable terms are on the left hand side.

x^{2}+1-y=0

Subtract y from both sides.

x=\frac{0±\sqrt{0^{2}-4\left(1-y\right)}}{2}

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 1-y for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

x=\frac{0±\sqrt{-4\left(1-y\right)}}{2}

Square 0.

x=\frac{0±\sqrt{4y-4}}{2}

Multiply -4 times 1-y.

x=\frac{0±2\sqrt{y-1}}{2}

Take the square root of -4+4y.

x=\sqrt{y-1}

Now solve the equation x=\frac{0±2\sqrt{y-1}}{2} when ± is plus.

x=-\sqrt{y-1}

Now solve the equation x=\frac{0±2\sqrt{y-1}}{2} when ± is minus.

x=\sqrt{y-1} x=-\sqrt{y-1}

The equation is now solved.

Examples

Quadratic equation

{ x } ^ { 2 } - 4 x - 5 = 0

$x_{2}−4x−5=0$

Trigonometry

4 \sin \theta \cos \theta = 2 \sin \theta

$4sinθcosθ=2sinθ$

Linear equation

y = 3x + 4

$y=3x+4$

Arithmetic

699 * 533

$699∗533$

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]

$[25 34 ][2−1 01 35 ]$

Simultaneous equation

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

${8x+2y=467x+3y=47 $

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

$dxd (x−5)(3x_{2}−2) $

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

$∫_{0}xe_{−x_{2}}dx$

Limits

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

$x→−3lim x_{2}+2x−3x_{2}−9 $