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

Expand and Simplify: Simplify the equation by expanding the squared term. We have the equation (9x-2)-(9x-2)^(2)=0. Let's expand the squared term. (9x-2) - (9x-2)*(9x-2) = 0Distribute Negative Sign: Distribute the negative sign through the squared term. We need to apply the negative sign to each term in the squared expression. (9x-2) - [(9x-2)*(9x-2)] = 0 (9x-2) - [81x^2 - 36x + 4] = 0Combine Like Terms: Combine like terms. Now we combine the like terms on the left side of the equation. 9x - 2 - 81x^2 + 36x - 4 = 0Factor Out Common Factor: Continue combining like terms. Combine the x terms and the constant terms. -81x^2 + 45x - 6 = 0Find Quadratic Factors: Factor out the greatest common factor. We can factor out a 3 from each term. -27x^2 + 15x - 2 = 0Apply Quadratic Formula: Look for factors of the quadratic equation. This is a quadratic equation in the form ax^2 + bx + c = 0. We need to find factors or use the quadratic formula to solve for x. However, this equation does not factor nicely, so we will use the quadratic formula. x = [-b ± sqrt(b^2 - 4ac)] / (2a)Simplify and Solve: Apply the quadratic formula. Let's plug in the values a = -27, b = 15, and c = -2 into the quadratic formula. x = [-15 ± sqrt(15^2 - 4(-27)(-2))] / (2(-27)) x = [-15 ± sqrt(225 - 216)] / (-54)Simplify under the square root and solve for x. x = [-15 ± sqrt(9)] / (-54) x = [-15 ± 3] / (-54)Solve for the two possible values of x. x = (-15 + 3) / (-54) or x = (-15 - 3) / (-54) x = -12 / -54 or x = -18 / -54Simplify both fractions. x = 2 / 9 or x = 1 / 3

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Solve for all values of
x :

(9x-2)-(9x-2)^(2)=0
Answer:
x=

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

(9 x-2)-(9 x-2)^{2}=0

\newline

Answer:

x=

Expand and Simplify: Simplify the equation by expanding the squared term. $\newline$ We have the equation $(9x-2)-(9x-2)^{2}=0$ . Let's expand the squared term. $\newline$ $(9x-2) - (9x-2)\cdot(9x-2) = 0$
Distribute Negative Sign: Distribute the negative sign through the squared term. $\newline$ We need to apply the negative sign to each term in the squared expression. $\newline$ $(9x-2) - [(9x-2)*(9x-2)] = 0$ $\newline$ $(9x-2) - [81x^2 - 36x + 4] = 0$
Combine Like Terms: Combine like terms. $\newline$ Now we combine the like terms on the left side of the equation. $\newline$ $9x - 2 - 81x^2 + 36x - 4 = 0$
Factor Out Common Factor: Continue combining like terms. $\newline$ Combine the $x$ terms and the constant terms. $\newline$ $-81x^2 + 45x - 6 = 0$
Find Quadratic Factors: Factor out the greatest common factor. $\newline$ We can factor out a $3$ from each term. $\newline$ $-27x^2 + 15x - 2 = 0$
Apply Quadratic Formula: Look for factors of the quadratic equation. $\newline$ This is a quadratic equation in the form $ax^2 + bx + c = 0$ . We need to find factors or use the quadratic formula to solve for $x$ . However, this equation does not factor nicely, so we will use the quadratic formula. $\newline$ $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Simplify and Solve: Apply the quadratic formula. $\newline$ Let's plug in the values $a = -27$ , $b = 15$ , and $c = -2$ into the quadratic formula. $\newline$ $x = \frac{-15 \pm \sqrt{15^2 - 4(-27)(-2)}}{2(-27)}$ $\newline$ $x = \frac{-15 \pm \sqrt{225 - 216}}{-54}$
Simplify and Solve: Apply the quadratic formula. $\newline$ Let's plug in the values $a = -27$ , $b = 15$ , and $c = -2$ into the quadratic formula. $\newline$ $x = \frac{-15 \pm \sqrt{15^2 - 4(-27)(-2)}}{2(-27)}$ $\newline$ $x = \frac{-15 \pm \sqrt{225 - 216}}{-54}$ Simplify under the square root and solve for x. $\newline$ $x = \frac{-15 \pm \sqrt{9}}{-54}$ $\newline$ $x = \frac{-15 \pm 3}{-54}$
Simplify and Solve: Apply the quadratic formula. $\newline$ Let's plug in the values $a = -27$ , $b = 15$ , and $c = -2$ into the quadratic formula. $\newline$ $x = \frac{-15 \pm \sqrt{15^2 - 4(-27)(-2)}}{2(-27)}$ $\newline$ $x = \frac{-15 \pm \sqrt{225 - 216}}{-54}$ Simplify under the square root and solve for x. $\newline$ $x = \frac{-15 \pm \sqrt{9}}{-54}$ $\newline$ $x = \frac{-15 \pm 3}{-54}$ Solve for the two possible values of x. $\newline$ $x = \frac{(-15 + 3)}{-54}$ or $x = \frac{(-15 - 3)}{-54}$ $\newline$ $x = -12 / -54$ or $b = 15$ $0$
Simplify and Solve: Apply the quadratic formula. $\newline$ Let's plug in the values $a = -27$ , $b = 15$ , and $c = -2$ into the quadratic formula. $\newline$ $x = \frac{-15 \pm \sqrt{15^2 - 4(-27)(-2)}}{2(-27)}$ $\newline$ $x = \frac{-15 \pm \sqrt{225 - 216}}{-54}$ Simplify under the square root and solve for x. $\newline$ $x = \frac{-15 \pm \sqrt{9}}{-54}$ $\newline$ $x = \frac{-15 \pm 3}{-54}$ Solve for the two possible values of x. $\newline$ $x = \frac{(-15 + 3)}{(-54)}$ or $x = \frac{(-15 - 3)}{(-54)}$ $\newline$ $x = \frac{-12}{-54}$ or $b = 15$ $0$ Simplify both fractions. $\newline$ $b = 15$ $1$ or $b = 15$ $2$