Algebra Examples

$0$ , $- 3$ , $\sqrt{2}$

Step 1

$x = 0$ and $x = - 3$ are the two real distinct solutions for the quadratic equation, which means that $x - 0$ and $x + 3$ are the factors of the quadratic equation.

$(x - 0) (x + 3) = 0$

Step 2

Subtract $0$ from $x$ .

$x (x + 3) = 0$

Step 3

Apply the distributive property.

$x \cdot x + x \cdot 3 = 0$

Step 4

Simplify the expression.

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Step 4.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 = 0$

Step 4.2

Move $3$ to the left of $x$ .

$x^{2} + 3 x = 0$

Step 5

The standard quadratic equation using the given set of solutions ${0, - 3, \sqrt{2}}$ is $y = x^{2} + 3 x$ .

$y = x^{2} + 3 x$

Step 6