Solve for all values of x : 7(4x+3)-(4x+3)^(2)=0 Answer: x=

Expand Equation: Expand the equation to simplify it. We have the equation 7(4x+3)-(4x+3)²=0. Let's first expand the squared term (4x+3)². (4x+3)² = (4x+3)(4x+3) = 16x² + 12x + 12x + 9 = 16x² + 24x + 9Substitute Expanded Term: Substitute the expanded squared term back into the equation. Now we substitute the expanded (4x+3)² back into the original equation: 7(4x+3) - (16x² + 24x + 9) = 0Expand and Combine Terms: Expand the remaining term and combine like terms. Next, we expand 7(4x+3) and subtract (16x² + 24x + 9) from it: 7(4x+3) = 28x + 21 So the equation becomes: 28x + 21 - (16x² + 24x + 9) = 0Distribute Negative Sign: Distribute the negative sign through the second set of parentheses. We need to distribute the negative sign through the second set of parentheses: 28x + 21 - 16x² - 24x - 9 = 0Combine Like Terms: Combine like terms to form a quadratic equation. Now we combine like terms: -16x² + (28x - 24x) + (21 - 9) = 0 -16x² + 4x + 12 = 0Factor Quadratic Equation: Factor the quadratic equation. We need to factor the quadratic equation -16x² + 4x + 12 = 0. We can factor out a 4: 4(-4x² + x + 3) = 0 Now we need to factor the quadratic expression in the parentheses. However, this expression does not factor nicely, so we may have made a mistake. Let's go back and check our previous steps.

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Solve for all values of
x :

7(4x+3)-(4x+3)^(2)=0
Answer:
x=

Solve for all values of $x$ : $\newline$ $7(4 x+3)-(4 x+3)^{2}=0$ $\newline$ Answer: $x=$

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Math Problems

Algebra 2

Composition of linear and quadratic functions: find an equation

Full solution

Q. Solve for all values of

x

\newline

7(4 x+3)-(4 x+3)^{2}=0

\newline

Answer:

x=

Expand Equation: Expand the equation to simplify it. $\newline$ We have the equation $7(4x+3)-(4x+3)^2=0$ . Let's first expand the squared term $(4x+3)^2$ . $\newline$ $(4x+3)^2 = (4x+3)(4x+3) = 16x^2 + 12x + 12x + 9 = 16x^2 + 24x + 9$
Substitute Expanded Term: Substitute the expanded squared term back into the equation. $\newline$ Now we substitute the expanded $(4x+3)^2$ back into the original equation: $\newline$ $7(4x+3) - (16x^2 + 24x + 9) = 0$
Expand and Combine Terms: Expand the remaining term and combine like terms. $\newline$ Next, we expand $7(4x+3)$ and subtract $(16x^2 + 24x + 9)$ from it: $\newline$ $7(4x+3) = 28x + 21$ $\newline$ So the equation becomes: $\newline$ $28x + 21 - (16x^2 + 24x + 9) = 0$
Distribute Negative Sign: Distribute the negative sign through the second set of parentheses. $\newline$ We need to distribute the negative sign through the second set of parentheses: $\newline$ $28x + 21 - 16x^2 - 24x - 9 = 0$
Combine Like Terms: Combine like terms to form a quadratic equation. $\newline$ Now we combine like terms: $\newline$ $-16x^2 + (28x - 24x) + (21 - 9) = 0$ $\newline$ $-16x^2 + 4x + 12 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ We need to factor the quadratic equation $-16x^2 + 4x + 12 = 0$ . We can factor out a $4$ : $\newline$ $4(-4x^2 + x + 3) = 0$ $\newline$ Now we need to factor the quadratic expression in the parentheses. However, this expression does not factor nicely, so we may have made a mistake. Let's go back and check our previous steps.