Which equation has the same solution as x^(2)+17 x-6=5 ? (x-8.5)^(2)=-61.25 (x-8.5)^(2)=83.25 (x+8.5)^(2)=-61.25 (x+8.5)^(2)=83.25

Question

Which equation has the same solution as  x^(2)+17 x-6=5 ?  (x-8.5)^(2)=-61.25  (x-8.5)^(2)=83.25  (x+8.5)^(2)=-61.25  (x+8.5)^(2)=83.25

Bytelearn · Accepted Answer

Simplify Equation: Step Title: Simplify the Given Equation Concise Step Description: Simplify the given equation by moving all terms to one side to set the equation to zero. Step Calculation: x^2 + 17x - 6 - 5 = 0 => x^2 + 17x - 11 = 0Identify Coefficients: Step Title: Identify the Coefficients of the Simplified Equation Concise Step Description: Identify the coefficients of the simplified quadratic equation. Step Calculation: Coefficients are 1, 17, -11Compare with Options: Step Title: Compare the Given Options with the Simplified Equation Concise Step Description: Compare each option to see which one can be simplified to the form of the given equation. Step Calculation:  Option 1: (x - 8.5)^2 = -61.25 => x^2 - 17x + 72.25 = -61.25 => x^2 - 17x + 133.5 = 0 Option 2: (x - 8.5)^2 = 83.25 => x^2 - 17x + 72.25 = 83.25 => x^2 - 17x - 11 = 0 Option 3: (x + 8.5)^2 = -61.25 => x^2 + 17x + 72.25 = -61.25 => x^2 + 17x + 133.5 = 0 Option 4: (x + 8.5)^2 = 83.25 => x^2 + 17x + 72.25 = 83.25 => x^2 + 17x - 11 = 0Determine Correct Option: Step Title: Determine the Correct Option Concise Step Description: Determine which option, when simplified, matches the simplified given equation x^2 + 17x - 11 = 0. Step Calculation: The correct option is Option 4: (x + 8.5)^2 = 83.25, which simplifies to x^2 + 17x - 11 = 0.

Which equation has the same solution as $x^{2}+17 x-6=5$ ? $\newline$ $(x-8.5)^{2}=-61.25$ $\newline$ $(x-8.5)^{2}=83.25$ $\newline$ $(x+8.5)^{2}=-61.25$ $\newline$ $(x+8.5)^{2}=83.25$

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