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How do you solve 2x213x7=0?

Answer
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Hint: As the given is the quadratic equation so we will solve it by using the quadratic formula. We know that for an equation of the form ax2+bx+c=0 the quadratic formula is given as x=b±b24ac2a . By substituting the values and solving further we will get the desired answer.

Complete step-by-step solution:
We have been given an equation 2x213x7=0.
We have to solve the given equation.
We know that quadratic formula for the general equation ax2+bx+c=0 is given as x=b±b24ac2a.
Now, by comparing the given equation with general equation we get the values
a=2,b=13,c=7
Now, substituting the values in the formula we will get
x=(13)±(13)24×2×(7)2×2
Now, simplifying the above obtained equation we will get
x=13±169+564x=13±2254
Now, simplifying the above obtained equation we will get
x=13±154
Now, considering both signs one by one we will get
x=13+154,x=13154
Now, simplifying the above obtained equation we will get
x=284,x=24x=7,x=12
Hence we get the solution of the given quadratic equation as x=7,12.

Note: Alternatively we can also solve the given equation by splitting the middle term and find the factors. Then we can equate each factor to zero and solve the equation for x.
We have 2x213x7=0.
Now, splitting the middle term of the given equation we will get
2x2(14xx)7=0
Now, simplifying the above obtained equation we will get
2x214x+x7=0
Now, taking common terms out we will get
2x(x7)+1(x7)=0
Again taking common factor out we will get
(x7)(2x+1)=0
Now, equating each factor to zero we will get
x7=0 and 2x+1=0x=7 and x=12
Hence above is the required solution.