Solve a(x - 5)(x + 4) = 0; 1 - 502x + 9 = 1 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$a(x-5)(x+4)=0; 1-502x+9=1$$

Solve for a, x

$x=\frac{9}{502}\approx 0.017928287$
$a=0$

Solution Steps

Consider the second equation. Add $1$ and $9$ to get $10$.

$$10-502x=1$$

Subtract $10$ from both sides.

$$-502x=1-10$$

Subtract $10$ from $1$ to get $-9$.

$$-502x=-9$$

Divide both sides by $-502$.

$$x=\frac{-9}{-502}$$

Fraction $\frac{-9}{-502}$ can be simplified to $\frac{9}{502}$ by removing the negative sign from both the numerator and the denominator.

$$x=\frac{9}{502}$$

Consider the first equation. Insert the known values of variables into the equation.

$$a\left(\frac{9}{502}-5\right)\left(\frac{9}{502}+4\right)=0$$

Subtract $5$ from $\frac{9}{502}$ to get $-\frac{2501}{502}$.

$$a\left(-\frac{2501}{502}\right)\left(\frac{9}{502}+4\right)=0$$

Add $\frac{9}{502}$ and $4$ to get $\frac{2017}{502}$.

$$a\left(-\frac{2501}{502}\right)\times \frac{2017}{502}=0$$

Multiply $-\frac{2501}{502}$ and $\frac{2017}{502}$ to get $-\frac{5044517}{252004}$.

$$a\left(-\frac{5044517}{252004}\right)=0$$

Multiply both sides by $-\frac{252004}{5044517}$, the reciprocal of $-\frac{5044517}{252004}$. Anything times zero gives zero.

$$a=0$$

The system is now solved.

$$a=0$$ $$x=\frac{9}{502}$$