Rewrite in standard form: Rewrite the equation in standard quadratic form. The standard form of a quadratic equation is ax^2 + bx + c = 0. To achieve this, we need to move all terms to one side of the equation. So, we subtract 250 from both sides of the equation 60x - 2x^2 = 250 to get -2x^2 + 60x - 250 = 0.Simplify by dividing: Simplify the equation by dividing all terms by -2 to make the x^2 coefficient positive. Dividing each term by -2 gives us x^2 - 30x + 125 = 0.Factor the equation: Factor the quadratic equation. We need to find two numbers that multiply to 125 and add up to -30. These numbers are -25 and -5. So, we can write the equation as (x - 25)(x - 5) = 0.Solve using zero product property: Solve for x using the zero product property. The zero product property states that if a product of two factors is zero, then at least one of the factors must be zero. Setting each factor equal to zero gives us two equations: x - 25 = 0 and x - 5 = 0.Solve for x: Solve each equation for x. For x - 25 = 0, adding 25 to both sides gives us x = 25. For x - 5 = 0, adding 5 to both sides gives us x = 5.

Algebra 2

Factor quadratics

Full solution

60x - 2x^2 = 250

Rewrite in standard form: Rewrite the equation in standard quadratic form. $\newline$ The standard form of a quadratic equation is $ax^2 + bx + c = 0$ . To achieve this, we need to move all terms to one side of the equation. $\newline$ So, we subtract $250$ from both sides of the equation $60x - 2x^2 = 250$ to get $-2x^2 + 60x - 250 = 0$ .
Simplify by dividing: Simplify the equation by dividing all terms by $-2$ to make the $x^2$ coefficient positive. $\newline$ Dividing each term by $-2$ gives us $x^2 - 30x + 125 = 0$ .
Factor the equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $125$ and add up to $-30$ . These numbers are $-25$ and $-5$ . $\newline$ So, we can write the equation as $(x - 25)(x - 5) = 0$ .
Solve using zero product property: Solve for $x$ using the zero product property. $\newline$ The zero product property states that if a product of two factors is zero, then at least one of the factors must be zero. $\newline$ Setting each factor equal to zero gives us two equations: $x - 25 = 0$ and $x - 5 = 0$ .
Solve for x: Solve each equation for x. $\newline$ For $x - 25 = 0$ , adding $25$ to both sides gives us $x = 25$ . $\newline$ For $x - 5 = 0$ , adding $5$ to both sides gives us $x = 5$ .