Question

solve by factorisation method? 1) 4x²-4x+1=0​

Answer 1

Answer:

Step-by-step explanation:

4x²-4x+1=0

(2x)^2-2(2x)(1)+(1)^2=0

(2x-1)^2=0

Taking square root on both sides

2x-1=0

2x=1

X=1/2

Answer 2

Method 1 - Solve by Factoring

Let's solve your equation step-by-step.

$\sf 4x^2-4x+1=0$

Step 1: Factor left side of the equation.

$\sf (2x-1)(2x-1)=0$

Step 2: Set factors equal to 0.

$\sf 2x-1=0$

$\sf 2x =1$

$\sf x=\frac{1}{2}$

$\sf x=0.5$

Method 2 - Solve with Quadratic Formula

Let's solve your equation step-by-step.

$\sf 4x^2-4x+1=0$

$\sf For\ this\ equation\ \rightarrow \\a=4\\ b=-4 \\ c=1$

Step 1: Use quadratic formula with a = 4, b = -4, c = 1.

$\sf x=\frac{-b\± \sqrt{b^{2}-4ac} }{2a}$

$\sf x=\frac{-(-4)\± \sqrt{(-4)^{2}-4(4)(1)} }{2(4)}$

$\sf x=\frac{4\± \sqrt{0} }{8}$

$\sf x=0.5$

Method 3 - Solve by Completing the Square

Let's solve your equation step-by-step.

$\sf 4x^2-4x+1=0$

Step 1: Subtract 1 from both sides.

$\sf 4x^2-4x+1-1=0-1$

$\sf 4x^{2}-4x=-1$

Step 2: Since the coefficient of $\sf 4x^{2}$ is 4, divide both sides by 4.

$\sf \frac{4x^2-4x}{4} =\frac{-1}{4}$

$\sf x^2-x=\frac{-1}{4}$

Step 3: The coefficient of -x is -1. Let b = -1.

Then we need to add $\sf (\frac{b}{2} )^2=\frac{1}{4}$ to both sides to complete the square.

Add $\sf \frac{1}{4}$ to both sides.

$\sf x^2-x+\frac{1}{4} =\frac{-1}{4}+\frac{1}{4}$

$\sf x^2-x+\frac{1}{4}=0$

Step 4: Factor left side.

$\sf (x\frac{-1}{2})^2=0$

Step 5: Take the square root.

$\sf x\frac{-1}{2} =\± \sqrt{0}$

Step 6: Add $\sf \frac{1}{2}$ to both sides.

$\sf x\frac{-1}{2} +\frac{1}{2} =\frac{1}{2} \± \sqrt{0}$

$\sf x=\frac{1}{2}\± \sqrt{0}$

$\sf x=0.5$

$\sf \bf \therefore\ x=0.5 \ in \ the \ equation \rightarrow 4x^2-4x+1=0$