Solve for all values of x : (4x+9)^(2)+(4x+9)=0 Answer: x=

Identify quadratic equation: Identify the quadratic equation to solve. We have the equation (4x+9)² + (4x+9) = 0. This is a quadratic equation in the form of a quadratic trinomial set equal to zero.Factor the equation: Factor the quadratic equation. Notice that (4x+9) is a common factor in both terms of the equation. We can factor it out: (4x+9)((4x+9) + 1) = 0 This simplifies to: (4x+9)(4x+9 + 1) = 0 (4x+9)(4x+10) = 0Apply zero-product property: Apply the zero-product property. If the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero: 4x+9 = 0 or 4x+10 = 0Solve for x: Solve each equation for x. First equation: 4x+9 = 0 Subtract 9 from both sides: 4x = -9 Divide by 4: x = -9/4 Second equation: 4x+10 = 0 Subtract 10 from both sides: 4x = -10 Divide by 4: x = -10/4 Simplify: x = -5/2

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Solve for all values of
x :

(4x+9)^(2)+(4x+9)=0
Answer:
x=

Solve for all values of $x$ : $\newline$ $(4 x+9)^{2}+(4 x+9)=0$ $\newline$ Answer: $x=$

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Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. Solve for all values of

x

\newline

(4 x+9)^{2}+(4 x+9)=0

\newline

Answer:

x=

Identify quadratic equation: Identify the quadratic equation to solve. $\newline$ We have the equation $(4x+9)^2 + (4x+9) = 0$ . This is a quadratic equation in the form of a quadratic trinomial set equal to zero.
Factor the equation: Factor the quadratic equation. $\newline$ Notice that $(4x+9)$ is a common factor in both terms of the equation. We can factor it out: $\newline$ $(4x+9)((4x+9) + 1) = 0$ $\newline$ This simplifies to: $\newline$ $(4x+9)(4x+9 + 1) = 0$ $\newline$ $(4x+9)(4x+10) = 0$
Apply zero-product property: Apply the zero-product property. $\newline$ If the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero: $\newline$ $4x+9 = 0$ or $4x+10 = 0$
Solve for x: Solve each equation for x. $\newline$ First equation: $4x+9 = 0$ $\newline$ Subtract $9$ from both sides: $4x = -9$ $\newline$ Divide by $4$ : $x = -\frac{9}{4}$ $\newline$ Second equation: $4x+10 = 0$ $\newline$ Subtract $10$ from both sides: $4x = -10$ $\newline$ Divide by $4$ : $x = -\frac{10}{4}$ $\newline$ Simplify: $x = -\frac{5}{2}$