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Factor the trinomial by $-1$ for an easier handling
Factor the trinomial $-\left(x^2-7x+10\right)$ finding two numbers that multiply to form $10$ and added form $-7$
Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values
Factor the trinomial $\left(x^2-7x+10\right)$ finding two numbers that multiply to form $10$ and added form $-7$
Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values
Apply the formula: $-x=a$$\to x=-a$, where $a=0$ and $x=\left(x-2\right)\left(x-5\right)$
Break the equation in $2$ factors and set each factor equal to zero, to obtain simpler equations
Solve the equation ($1$)
Apply the formula: $x+a=b$$\to x+a-a=b-a$, where $a=-2$, $b=0$, $x+a=b=x-2=0$ and $x+a=x-2$
Apply the formula: $x+a+c=b+f$$\to x=b-a$, where $a=-2$, $b=0$, $c=2$ and $f=2$
Solve the equation ($2$)
Apply the formula: $x+a=b$$\to x+a-a=b-a$, where $a=-5$, $b=0$, $x+a=b=x-5=0$ and $x+a=x-5$
Apply the formula: $x+a+c=b+f$$\to x=b-a$, where $a=-5$, $b=0$, $c=5$ and $f=5$
Combining all solutions, the $2$ solutions of the equation are
