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Question
Math
Posted 3 months ago
Solve.
6+2x23x=8x2
6+2 x^{2}-3 x=8 x^{2}


Choose 1 answer:
(A) x=3,12x=3,-\frac{1}{2}
(B) x=5±5716x=\frac{5 \pm \sqrt{57}}{16}
(C) x=1±174x=\frac{1 \pm \sqrt{17}}{-4}
(D) x=4±343x=\frac{-4 \pm \sqrt{34}}{3}
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Answer from Sia
Posted 3 months ago
Solution by Steps
step 2
Simplify the equation by combining like terms: 2x28x2=6x22x^2 - 8x^2 = -6x^2 and 66 remains unchanged, so we have 6x23x+6=0-6x^2 - 3x + 6 = 0
step 3
Divide the entire equation by 3-3 to simplify: 6x233x3+63=0\frac{-6x^2}{-3} - \frac{3x}{-3} + \frac{6}{-3} = 0 which simplifies to 2x2+x2=02x^2 + x - 2 = 0
step 4
Factor the quadratic equation: (2x1)(x+2)=0(2x - 1)(x + 2) = 0
step 5
Solve for xx by setting each factor equal to zero: 2x1=02x - 1 = 0 and x+2=0x + 2 = 0
step 6
Solve the first equation 2x1=02x - 1 = 0 for xx: x=12x = \frac{1}{2}
step 7
Solve the second equation x+2=0x + 2 = 0 for xx: x=2x = -2
A
Key Concept
Solving quadratic equations by factoring
Explanation
To solve a quadratic equation, we can move all terms to one side to set the equation to zero, factor the quadratic, and then solve for xx by setting each factor equal to zero.

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