Step-by-step Solution

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Final Answer

$x=5,\:x=2$

Step-by-step Solution

Problem to solve:

$-x^2+7x-10=0$
1

For a simpler handling of the equation, change the sign of all terms, multiplying the entire whole by $-1$

$x^2-7x+10=0$
2

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=1$, $b=-7$ and $c=10$. Then substitute the values of the coefficients of the equation in the quadratic formula:

• $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{7\pm 3}{2}$
3

To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)

$x=\frac{7+3}{2},\:x=\frac{7-3}{2}$
4

Subtract the values $7$ and $-3$

$x=\frac{7+3}{2},\:x=\frac{4}{2}$
5

Add the values $7$ and $3$

$x=\frac{10}{2},\:x=\frac{4}{2}$
6

Divide $10$ by $2$

$x=5,\:x=\frac{4}{2}$
7

Divide $4$ by $2$

$x=5,\:x=2$

Final Answer

$x=5,\:x=2$
$-x^2+7x-10=0$

Main topic:

Quadratic equations

~ 0.05 s