Which equation has the same solution as x^(2)-19 x-8=2 ? (x-9.5)^(2)=-80.25 (x+9.5)^(2)=100.25 (x+9.5)^(2)=-80.25 (x-9.5)^(2)=100.25

Simplify Equation: Simplify the given equation by moving all terms to one side to set the equation equal to zero. x^2 - 19x - 8 - 2 = 0 x^2 - 19x - 10 = 0Find Vertex Form: Find the vertex form of the quadratic equation. The vertex form is given by (x - h)^2 = k, where (h, k) is the vertex of the parabola. To find h, use the formula h = -b/(2a), where a is the coefficient of x^2 and b is the coefficient of x. In this case, a = 1 and b = -19, so h = -(-19)/(2*1) = 19/2 = 9.5.Calculate Vertex Coordinates: Calculate the value of k by substituting h back into the original equation. k = (9.5)^2 - 19(9.5) - 10 k = 90.25 - 180.5 - 10 k = -90.25 - 10 k = -100.25Write Vertex Form Equation: Write the equation in vertex form using the values of h and k. (x - 9.5)^2 = -100.25Compare with Choices: Compare the vertex form equation with the given choices to find the one that matches. The correct choice is (x - 9.5)^2 = -100.25, which is not listed among the choices provided. However, if we add 100.25 to both sides of the equation, we get: (x - 9.5)^2 + 100.25 = 0 (x - 9.5)^2 = -100.25Correct Mistake: Realize that there has been a mistake in the previous step. The correct step should be to add 100.25 to both sides of the equation to get: (x - 9.5)^2 = 100.25 This matches one of the given choices.

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Which equation has the same solution as
x^(2)-19 x-8=2 ?

(x-9.5)^(2)=-80.25

(x+9.5)^(2)=100.25

(x+9.5)^(2)=-80.25

(x-9.5)^(2)=100.25

Which equation has the same solution as $x^{2}-19 x-8=2$ ? $\newline$ $(x-9.5)^{2}=-80.25$ $\newline$ $(x+9.5)^{2}=100.25$ $\newline$ $(x+9.5)^{2}=-80.25$ $\newline$ $(x-9.5)^{2}=100.25$

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Q. Which equation has the same solution as

x^{2}-19 x-8=2

\newline

(x-9.5)^{2}=-80.25

\newline

(x+9.5)^{2}=100.25

\newline

(x+9.5)^{2}=-80.25

\newline

(x-9.5)^{2}=100.25

Simplify Equation: Simplify the given equation by moving all terms to one side to set the equation equal to zero. $\newline$ $x^2 - 19x - 8 - 2 = 0$ $\newline$ $x^2 - 19x - 10 = 0$
Find Vertex Form: Find the vertex form of the quadratic equation. The vertex form is given by $(x - h)^2 = k$ , where $(h, k)$ is the vertex of the parabola. $\newline$ To find $h$ , use the formula $h = -b/(2a)$ , where $a$ is the coefficient of $x^2$ and $b$ is the coefficient of $x$ . $\newline$ In this case, $a = 1$ and $b = -19$ , so $(h, k)$ $0$ .
Calculate Vertex Coordinates: Calculate the value of $k$ by substituting $h$ back into the original equation. $\newline$ $k = (9.5)^2 - 19(9.5) - 10$ $\newline$ $k = 90.25 - 180.5 - 10$ $\newline$ $k = -90.25 - 10$ $\newline$ $k = -100.25$
Write Vertex Form Equation: Write the equation in vertex form using the values of $h$ and $k$ . $(x - 9.5)^2 = -100.25$
Compare with Choices: Compare the vertex form equation with the given choices to find the one that matches. $\newline$ The correct choice is $(x - 9.5)^2 = -100.25$ , which is not listed among the choices provided. However, if we add $100.25$ to both sides of the equation, we get: $\newline$ $(x - 9.5)^2 + 100.25 = 0$ $\newline$ $(x - 9.5)^2 = -100.25$
Correct Mistake: Realize that there has been a mistake in the previous step. The correct step should be to add $100.25$ to both sides of the equation to get: $\newline$ $(x - 9.5)^2 = 100.25$ $\newline$ This matches one of the given choices.