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Which equation has the same solution as 
x^(2)+13 x+10=2 ?

(x-6.5)^(2)=-50.25

(x+6.5)^(2)=34.25

(x+6.5)^(2)=-50.25

(x-6.5)^(2)=34.25

Which equation has the same solution as x2+13x+10=2 x^{2}+13 x+10=2 ?\newline(x6.5)2=50.25 (x-6.5)^{2}=-50.25 \newline(x+6.5)2=34.25 (x+6.5)^{2}=34.25 \newline(x+6.5)2=50.25 (x+6.5)^{2}=-50.25 \newline(x6.5)2=34.25 (x-6.5)^{2}=34.25

Full solution

Q. Which equation has the same solution as x2+13x+10=2 x^{2}+13 x+10=2 ?\newline(x6.5)2=50.25 (x-6.5)^{2}=-50.25 \newline(x+6.5)2=34.25 (x+6.5)^{2}=34.25 \newline(x+6.5)2=50.25 (x+6.5)^{2}=-50.25 \newline(x6.5)2=34.25 (x-6.5)^{2}=34.25
  1. Simplify Equation: Simplify the given equation by moving all terms to one side to set the equation equal to zero.\newlinex2+13x+102=0x^2 + 13x + 10 - 2 = 0\newlinex2+13x+8=0x^2 + 13x + 8 = 0
  2. Factor Quadratic: Look for a way to factor the quadratic equation, if possible.\newlineWe need to find two numbers that multiply to 88 and add up to 1313. However, there are no such integer pairs, so we might need to complete the square or use the quadratic formula to solve for xx.
  3. Complete the Square: Complete the square for the quadratic equation x2+13x+8=0x^2 + 13x + 8 = 0.\newlineFirst, move the constant term to the other side:\newlinex2+13x=8x^2 + 13x = -8\newlineNext, take half of the coefficient of xx, which is 132\frac{13}{2}, square it, and add it to both sides of the equation:\newline(x+132)2=8+(132)2(x + \frac{13}{2})^2 = -8 + (\frac{13}{2})^2\newline(x+132)2=8+1694(x + \frac{13}{2})^2 = -8 + \frac{169}{4}\newline(x+132)2=(32+1694)(x + \frac{13}{2})^2 = (\frac{-32 + 169}{4})\newline(x+132)2=1374(x + \frac{13}{2})^2 = \frac{137}{4}
  4. Convert to Decimal: Convert the fraction to a decimal to compare with the given choices.\newline1374=34.25\frac{137}{4} = 34.25\newlineSo, the equation becomes:\newline(x+132)2=34.25(x + \frac{13}{2})^2 = 34.25
  5. Compare with Choices: Compare the completed square form of the equation with the given choices.\newlineWe have (x+132)2=34.25(x + \frac{13}{2})^2 = 34.25, and since 132\frac{13}{2} is 6.56.5, the equation can be written as:\newline(x+6.5)2=34.25(x + 6.5)^2 = 34.25\newlineThis matches one of the given choices.

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