Question

standard form of the quadratic equation x(x+1)=30 is​

Answer 1

Answer:

The standard form of the quadratic equation $x(x+1)=30$ is $1\cdot x^2+1\cdot x+(-30)=0$.

Step-by-step explanation:

The standard form of quadratic equation:

$ax^2+bx+c=0$ . . . . . (1)

where $a,\ b,\ c$ are the coefficients of $x^2,\ x$ and $x^0$ respectively.

Consider the given quadratic equation as follows:

$x(x+1)=30$

Simplify the left-hand side as follows:

$x^2+x=30$

Subtract the number $30$ from both the sides as follows:

$x^2+x-30=30-30$

$x^2+x-30=0$

Notice that,

The coefficient of $x^2$ is $1$.

The coefficient of $x$ is $1$.

The coefficient of $x^0$ is $-30$.

This implies $a=1$, $b=1$ and $c=-30$.

Now, Substitute the values $1$ for $a$, $1$ for $b$ and $-30$ for $c$ in the equation (1) as follows:

⇒ $(1)x^2+(1)x+(-30)c=0$

⇒ $1\cdot x^2+1\cdot x+(-30)=0$

Therefore, the standard form of the quadratic equation is $1\cdot x^2+1\cdot x+(-30)=0$.

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