Q. Which equation has the same solution as x2+13x+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
Simplify Equation: Simplify the given equation by moving all terms to one side to set the equation equal to zero.x2+13x+10−2=0x2+13x+8=0
Factor Quadratic: Look for a way to factor the quadratic equation, if possible.We need to find two numbers that multiply to 8 and add up to 13. However, there are no such integer pairs, so we might need to complete the square or use the quadratic formula to solve for x.
Complete the Square: Complete the square for the quadratic equation x2+13x+8=0.First, move the constant term to the other side:x2+13x=−8Next, take half of the coefficient of x, which is 213, square it, and add it to both sides of the equation:(x+213)2=−8+(213)2(x+213)2=−8+4169(x+213)2=(4−32+169)(x+213)2=4137
Convert to Decimal: Convert the fraction to a decimal to compare with the given choices.4137=34.25So, the equation becomes:(x+213)2=34.25
Compare with Choices: Compare the completed square form of the equation with the given choices.We have (x+213)2=34.25, and since 213 is 6.5, the equation can be written as:(x+6.5)2=34.25This matches one of the given choices.