Solve by Factoring x^(2)+14 x+48=0

Factor Quadratic Equation: Given the quadratic equation x^2 + 14x + 48 = 0, we need to factor it to find the solutions for x. To factor the quadratic equation, we look for two numbers that multiply to 48 (the constant term) and add up to 14 (the coefficient of the x term).Identify Factors: The two numbers that multiply to 48 and add up to 14 are 6 and 8. So we can write the quadratic equation as (x + 6)(x + 8) = 0.Apply Zero Product Property: Now, we apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero: x + 6 = 0 and x + 8 = 0.Solve for x: Solve each equation for x. For x + 6 = 0, we subtract 6 from both sides to get x = -6. For x + 8 = 0, we subtract 8 from both sides to get x = -8.

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Solve by Factoring $\newline$ $x^{2}+14 x+48=0$

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Q. Solve by Factoring

\newline

x^{2}+14 x+48=0

Factor Quadratic Equation: Given the quadratic equation $x^2 + 14x + 48 = 0$ , we need to factor it to find the solutions for $x$ . To factor the quadratic equation, we look for two numbers that multiply to $48$ (the constant term) and add up to $14$ (the coefficient of the $x$ term).
Identify Factors: The two numbers that multiply to $48$ and add up to $14$ are $6$ and $8$ . So we can write the quadratic equation as $(x + 6)(x + 8) = 0$ .
Apply Zero Product Property: Now, we apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. $\newline$ Therefore, we set each factor equal to zero: $x + 6 = 0$ and $x + 8 = 0$ .
Solve for x: Solve each equation for x. $\newline$ For $x + 6 = 0$ , we subtract $6$ from both sides to get $x = -6$ . $\newline$ For $x + 8 = 0$ , we subtract $8$ from both sides to get $x = -8$ .