Solve x1^2 + 4x^2^2 + x^2 - Socratic AI (ScanMath)

Question

Simplify the expression

x + 5 x^{2}

Evaluate

x \times 1^{2} + 4 x^{2} + x^{2}

1 raised to any power equals to 1

x \times 1 + 4 x^{2} + x^{2}

Any expression multiplied by 1 remains the same

x + 4 x^{2} + x^{2}

Solution

More Steps

Evaluate

4 x^{2} + x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(4 + 1) x^{2}

Add the numbers

5 x^{2}

x + 5 x^{2}

Show Solution

Factor the expression

x (1 + 5 x)

Evaluate

x \times 1^{2} + 4 x^{2} + x^{2}

1 raised to any power equals to 1

x \times 1 + 4 x^{2} + x^{2}

Any expression multiplied by 1 remains the same

x + 4 x^{2} + x^{2}

Add the terms

More Steps

Evaluate

4 x^{2} + x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(4 + 1) x^{2}

Add the numbers

5 x^{2}

x + 5 x^{2}

Rewrite the expression

x + x \times 5 x

Solution

x (1 + 5 x)

Show Solution

Find the roots

x_{1} = - \frac{1}{5}, x_{2} = 0

Alternative Form

x_{1} = - 0.2, x_{2} = 0

Evaluate

x \times 1^{2} + 4 x^{2} + x^{2}

To find the roots of the expression,set the expression equal to 0

x \times 1^{2} + 4 x^{2} + x^{2} = 0

1 raised to any power equals to 1

x \times 1 + 4 x^{2} + x^{2} = 0

Any expression multiplied by 1 remains the same

x + 4 x^{2} + x^{2} = 0

Add the terms

More Steps

Evaluate

x + 4 x^{2} + x^{2}

Add the terms

More Steps

Evaluate

4 x^{2} + x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(4 + 1) x^{2}

Add the numbers

5 x^{2}

x + 5 x^{2}

x + 5 x^{2} = 0

Factor the expression

More Steps

Evaluate

x + 5 x^{2}

Rewrite the expression

x + x \times 5 x

Factor out x from the expression

x (1 + 5 x)

x (1 + 5 x) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 1 + 5 x = 0

Solve the equation for x

More Steps

Evaluate

1 + 5 x = 0

Move the constant to the right-hand side and change its sign

5 x = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

5 x = - 1

Divide both sides

\frac{5 x}{5} = \frac{- 1}{5}

Divide the numbers

x = \frac{- 1}{5}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{5}

x = 0 x = - \frac{1}{5}

Solution

x_{1} = - \frac{1}{5}, x_{2} = 0

Alternative Form

x_{1} = - 0.2, x_{2} = 0

Show Solution

X1^2 + 4x^2^2 + x^2

Simplify the expression

Factor the expression

Find the roots