Asked by Isaiah Estilien on Apr 26, 2024
Verified
Solve the quadratic equation. x2+6x+25=0x ^ { 2 } + 6 x + 25 = 0x2+6x+25=0
A) x=14,x=−2x = 14 , x = - 2x=14,x=−2
B) x=1,x=−7x = 1 , x = - 7x=1,x=−7
C) x=−6±8ix = - 6 \pm 8 ix=−6±8i
D) x=6±8ix = 6 \pm 8 ix=6±8i
E) x=−3±4ix = - 3 \pm 4 ix=−3±4i
Quadratic Equation
A quadratic equation is represented as ax^2 + bx + c = 0, with a, b, and c being constant values and a not equal to zero.
- Determine the solutions to quadratic equations through the application of the quadratic formula.
Verified Answer
JH
Jessica HeathMay 02, 2024
Final Answer :
E
Explanation :
The quadratic equation x2+6x+25=0x^2 + 6x + 25 = 0x2+6x+25=0 can be solved using the quadratic formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac , where a=1a = 1a=1 , b=6b = 6b=6 , and c=25c = 25c=25 . Plugging these values in gives x=−6±(−6)2−4(1)(25)2(1)=−6±36−1002=−6±−642=−6±8i2=−3±4ix = \frac{-6 \pm \sqrt{(-6)^2 - 4(1)(25)}}{2(1)} = \frac{-6 \pm \sqrt{36 - 100}}{2} = \frac{-6 \pm \sqrt{-64}}{2} = \frac{-6 \pm 8i}{2} = -3 \pm 4ix=2(1)−6±(−6)2−4(1)(25)=2−6±36−100=2−6±−64=2−6±8i=−3±4i .
Learning Objectives
- Determine the solutions to quadratic equations through the application of the quadratic formula.