Solve (2x - 1) ^ 2 - 125 = 0 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(2x-1)^{2}-125=0$$

Solve for x

$x = \frac{5 \sqrt{5} + 1}{2} \approx 6.090169944$
$x=\frac{1-5\sqrt{5}}{2}\approx -5.090169944$

Steps by Finding Square Root

Add $125$ to both sides of the equation.

$$\left(2x-1\right)^{2}-125+125=125$$

Subtracting $125$ from itself leaves $0$.

$$\left(2x-1\right)^{2}=125$$

Take the square root of both sides of the equation.

$$2x-1=5\sqrt{5}$$ $$2x-1=-5\sqrt{5}$$

Add $1$ to both sides of the equation.

$$2x-1-\left(-1\right)=5\sqrt{5}-\left(-1\right)$$ $$2x-1-\left(-1\right)=-5\sqrt{5}-\left(-1\right)$$

Subtracting $-1$ from itself leaves $0$.

$$2x=5\sqrt{5}-\left(-1\right)$$ $$2x=-5\sqrt{5}-\left(-1\right)$$

Subtract $-1$ from $5\sqrt{5}$.

$$2x=5\sqrt{5}+1$$

Subtract $-1$ from $-5\sqrt{5}$.

$$2x=1-5\sqrt{5}$$

Divide both sides by $2$.

$$\frac{2x}{2}=\frac{5\sqrt{5}+1}{2}$$ $$\frac{2x}{2}=\frac{1-5\sqrt{5}}{2}$$

Dividing by $2$ undoes the multiplication by $2$.

$$x=\frac{5\sqrt{5}+1}{2}$$ $$x=\frac{1-5\sqrt{5}}{2}$$