Which equation has the same solution as x^(2)+17 x-18=6 ? (x+8.5)^(2)=-48.25 (x-8.5)^(2)=-48.25 (x-8.5)^(2)=96.25 (x+8.5)^(2)=96.25

Simplify the equation: First, let's simplify the given equation by moving all terms to one side to set the equation to zero. x^2 + 17x - 18 - 6 = 0 x^2 + 17x - 24 = 0Complete the square: Now, we need to find an equation that has the same solutions as x^2 + 17x - 24 = 0. To do this, we can complete the square to transform the given quadratic equation into a form that matches one of the choices. First, we calculate the value needed to complete the square. We take half of the coefficient of x, which is 17/2, and square it. (17/2)^2 = 8.5^2 = 72.25Add and subtract value: Next, we add and subtract this value inside the equation to complete the square. x^2 + 17x + 72.25 - 72.25 - 24 = 0 Now, we group the perfect square trinomial and the constants. (x + 8.5)^2 - 72.25 - 24 = 0Group the terms: Combine the constants to simplify the equation further. (x + 8.5)^2 - 96.25 = 0Combine the constants: Finally, we can rearrange the equation to match one of the choices. (x + 8.5)^2 = 96.25 This equation has the same solution as the original equation x^2 + 17x - 18 = 6.

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Which equation has the same solution as
x^(2)+17 x-18=6 ?

(x+8.5)^(2)=-48.25

(x-8.5)^(2)=-48.25

(x-8.5)^(2)=96.25

(x+8.5)^(2)=96.25

Which equation has the same solution as $x^{2}+17 x-18=6$ ? $\newline$ $(x+8.5)^{2}=-48.25$ $\newline$ $(x-8.5)^{2}=-48.25$ $\newline$ $(x-8.5)^{2}=96.25$ $\newline$ $(x+8.5)^{2}=96.25$

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Q. Which equation has the same solution as

x^{2}+17 x-18=6

\newline

(x+8.5)^{2}=-48.25

\newline

(x-8.5)^{2}=-48.25

\newline

(x-8.5)^{2}=96.25

\newline

(x+8.5)^{2}=96.25

Simplify the equation: First, let's simplify the given equation by moving all terms to one side to set the equation to zero. $\newline$ $x^2 + 17x - 18 - 6 = 0$ $\newline$ $x^2 + 17x - 24 = 0$
Complete the square: Now, we need to find an equation that has the same solutions as $x^2 + 17x - 24 = 0$ . To do this, we can complete the square to transform the given quadratic equation into a form that matches one of the choices. $\newline$ First, we calculate the value needed to complete the square. We take half of the coefficient of $x$ , which is $\frac{17}{2}$ , and square it. $\newline$ $(\frac{17}{2})^2 = 8.5^2 = 72.25$
Add and subtract value: Next, we add and subtract this value inside the equation to complete the square. $\newline$ $x^2 + 17x + 72.25 - 72.25 - 24 = 0$ $\newline$ Now, we group the perfect square trinomial and the constants. $\newline$ $(x + 8.5)^2 - 72.25 - 24 = 0$
Group the terms: Combine the constants to simplify the equation further. $\newline$ $(x + 8.5)^2 - 96.25 = 0$
Combine the constants: Finally, we can rearrange the equation to match one of the choices. $\newline$ $(x + 8.5)^2 = 96.25$ $\newline$ This equation has the same solution as the original equation $x^2 + 17x - 18 = 6$ .