### Most Used Actions

\mathrm{simplify} | \mathrm{solve\:for} | \mathrm{expand} | \mathrm{factor} | \mathrm{rationalize} |

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5x-2=0

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## Nonlinear equations

### Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

5*x^2-(1)=0

### Step by step solution :

### Step 1 :

#### Equation at the end of step 1 :

5x^{2}- 1 = 0

### Step 2 :

#### Trying to factor as a Difference of Squares :

Factoring: 5x^{2}-1

Theory : A difference of two perfect squares, A^{2} - B^{2} can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A^{2} - AB + BA - B^{2} =

A^{2}- AB + AB - B^{2} =

A^{2} - B^{2}

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 5 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

#### Equation at the end of step 2 :

5x^{2}- 1 = 0

### Step 3 :

#### Solving a Single Variable Equation :

Solve : 5x^{2}-1 = 0

Add 1 to both sides of the equation :

5x^{2} = 1

Divide both sides of the equation by 5:

x^{2} = 1/5 =

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 1/5

The equation has two real solutions

These solutions are x = ±√ = ±

### Two solutions were found :

x = ±√ = ±## &#;Explain how to solve 5x 2 - 3x = 25 by completing the square. What are the solutions?

Thanks, Mclovinhere's another way

5x ^2 - 3x = 25 divide through by 5

x^2 - (3/5)x = 5

Take (1/2) of (3/5) = 3/square it = 9/add to both sides

x^2 - (3/5)x + 9/ = 5 + 9/ factor the right side

(x - 3/10)^2 = / take both roots

x - 3/10 = ±√ [/]

x - 3/10 = ±√() /10 add 3/10 to both sides

x = [ 3 ±√ ] / 10

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## 2 5x solve :

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And Irka is right, thought Volodya: More than half of her.

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