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x^(2)-9x+10=32
D.
6x(x-8)=29

$x^{2}-9 x+10=32$ $\newline$ D. $6 x(x-8)=29$

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Solve complex trigonomentric equations

Full solution

Q.

x^{2}-9 x+10=32

\newline

D.

6 x(x-8)=29

Rewrite and Solve Quadratic Equation: Rewrite the first equation to set it equal to zero. $\newline$ $x^2 - 9x + 10 - 32 = 0$ $\newline$ $x^2 - 9x - 22 = 0$
Factor and Find Solutions: Factor the quadratic equation. $\newline$ $(x - 11)(x + 2) = 0$
Rewrite and Solve Another Quadratic Equation: Find the solutions for $x$ from the factored form. $x - 11 = 0$ or $x + 2 = 0$ $x = 11$ or $x = -2$
Use Quadratic Formula: Rewrite the second equation to set it equal to zero. $\newline$ $6x(x - 8) - 29 = 0$ $\newline$ $6x^2 - 48x - 29 = 0$
Calculate Discriminant: Attempt to factor the quadratic equation, but it doesn't factor nicely. $\newline$ We'll use the quadratic formula instead. $\newline$ $x = \frac{-(-48) \pm \sqrt{(-48)^2 - 4 \cdot 6 \cdot (-29)}}{2 \cdot 6}$
Calculate Solutions Using Formula: Calculate the discriminant ( $\Delta$ ) for the quadratic formula. $\newline$ $\Delta = (-48)^2 - 4\cdot6\cdot(-29)$ $\newline$ $\Delta = 2304 + 696$ $\newline$ $\Delta = 3000$
Simplify Solutions: Calculate the solutions using the quadratic formula. $\newline$ $x = \frac{48 \pm \sqrt{3000}}{12}$ $\newline$ $x = \frac{48 \pm 10\sqrt{30}}{12}$
Simplify Solutions: Calculate the solutions using the quadratic formula. $\newline$ $x = \frac{48 \pm \sqrt{3000}}{12}$ $\newline$ $x = \frac{48 \pm 10\sqrt{30}}{12}$ Simplify the solutions. $\newline$ $x = 4 \pm \frac{5\sqrt{30}}{3}$

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