Which equation has the same solution as x^(2)-5x-20=7 ? (x-2.5)^(2)=33.25 (x+2.5)^(2)=33.25 (x-2.5)^(2)=20.75 (x+2.5)^(2)=20.75

Question

Which equation has the same solution as  x^(2)-5x-20=7 ?  (x-2.5)^(2)=33.25  (x+2.5)^(2)=33.25  (x-2.5)^(2)=20.75  (x+2.5)^(2)=20.75

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Simplify Equation: First, let's simplify the given equation x^(2)-5x-20=7 by moving all terms to one side to set the equation to zero. x^(2) - 5x - 20 - 7 = 0 x^(2) - 5x - 27 = 0Expand Option 1: Now, let's look at the provided options to see which one, when expanded, will give us the same quadratic equation as x^(2) - 5x - 27 = 0. We will start by expanding the first option. Option 1: (x-2.5)^(2)=33.25 Expanding (x-2.5)^(2) gives us: x^(2) - 2*2.5*x + 2.5^2 = 33.25 x^(2) - 5x + 6.25 = 33.25 Now, subtract 33.25 from both sides to set the equation to zero: x^(2) - 5x + 6.25 - 33.25 = 0 x^(2) - 5x - 27 = 0 This matches our simplified equation.Check Option 2: Let's check the other options to ensure they do not also match the simplified equation. Option 2: (x+2.5)^(2)=33.25 Expanding (x+2.5)^(2) gives us: x^(2) + 2*2.5*x + 2.5^2 = 33.25 x^(2) + 5x + 6.25 = 33.25 Subtracting 33.25 from both sides: x^(2) + 5x + 6.25 - 33.25 = 0 x^(2) + 5x - 27 ≠ 0 This does not match our simplified equation.Check Option 3: Option 3: (x-2.5)^(2)=20.75 Expanding (x-2.5)^(2) gives us: x^(2) - 2*2.5*x + 2.5^2 = 20.75 x^(2) - 5x + 6.25 = 20.75 Subtracting 20.75 from both sides: x^(2) - 5x + 6.25 - 20.75 = 0 x^(2) - 5x - 14.5 ≠ 0 This does not match our simplified equation.Check Option 4: Option 4: (x+2.5)^(2)=20.75 Expanding (x+2.5)^(2) gives us: x^(2) + 2*2.5*x + 2.5^2 = 20.75 x^(2) + 5x + 6.25 = 20.75 Subtracting 20.75 from both sides: x^(2) + 5x + 6.25 - 20.75 = 0 x^(2) + 5x - 14.5 ≠ 0 This does not match our simplified equation.

Which equation has the same solution as $x^{2}-5 x-20=7$ ? $\newline$ $(x-2.5)^{2}=33.25$ $\newline$ $(x+2.5)^{2}=33.25$ $\newline$ $(x-2.5)^{2}=20.75$ $\newline$ $(x+2.5)^{2}=20.75$

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