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Which equation has the same solution as x^(2)-13 x+13=-2 ? (x+6.5)^(2)=27.25 (x-6.5)^(2)=-57.25 (x-6.5)^(2)=27.25 (x+6.5)^(2)=-57.25

Which equation has the same solution as x2−13x+13=−2 x^{2}-13 x+13=-2 ?\newline(x+6.5)2=27.25 (x+6.5)^{2}=27.25 \newline(x−6.5)2=−57.25 (x-6.5)^{2}=-57.25 \newline(x−6.5)2=27.25 (x-6.5)^{2}=27.25 \newline(x+6.5)2=−57.25 (x+6.5)^{2}=-57.25

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Full solution

Q. Which equation has the same solution as x2−13x+13=−2 x^{2}-13 x+13=-2 ?\newline(x+6.5)2=27.25 (x+6.5)^{2}=27.25 \newline(x−6.5)2=−57.25 (x-6.5)^{2}=-57.25 \newline(x−6.5)2=27.25 (x-6.5)^{2}=27.25 \newline(x+6.5)2=−57.25 (x+6.5)^{2}=-57.25
  1. Simplify Equation: Simplify the given equation by moving all terms to one side to set the equation to zero.\newlineWe start with the equation x2−13x+13=−2x^2 - 13x + 13 = -2 and add 22 to both sides to get:\newlinex2−13x+15=0x^2 - 13x + 15 = 0
  2. Pattern Matching: Look for a pattern in the given choices that matches the simplified equation.\newlineWe need to find which of the given equations, when simplified, will result in x2−13x+15=0x^2 - 13x + 15 = 0.
  3. First Choice Analysis: Analyze the first choice x + 6.5)^2 = 27.25\. Expanding \$x + 6.5)^2\ gives \$x^2 + 13x + 42.25. This does not match our simplified equation x2−13x+15x^2 - 13x + 15.
  4. Second Choice Analysis: Analyze the second choice x - \(6.55)^22 = −57-57.2525\. This choice is not valid because the square of a real number cannot be negative. Therefore, this equation does not have real solutions and cannot match our simplified equation.
  5. Third Choice Analysis: Analyze the third choice (x−6.5)2=27.25(x - 6.5)^2 = 27.25. Expanding (x−6.5)2(x - 6.5)^2 gives x2−13x+42.25x^2 - 13x + 42.25. This does not match our simplified equation x2−13x+15x^2 - 13x + 15.
  6. Fourth Choice Analysis: Analyze the fourth choice (x+6.5)2=−57.25(x + 6.5)^2 = -57.25. Similar to step 44, this choice is not valid because the square of a real number cannot be negative. Therefore, this equation does not have real solutions and cannot match our simplified equation.
  7. Reevaluate Choices: Realize that none of the given choices match the simplified equation x2−13x+15=0x^2 - 13x + 15 = 0. We must have made a mistake in our calculations or assumptions. Let's go back to step 33 and step 55 to recheck our expansions.

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