solve by factoring 2a^2+3=7a
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Start by rearranging into
2a^2-7a+3=0
Then either use the formula or it is possible to see the roots by inspection.
(a-3)(a-1/2)=0
2a^2+3=7a
2a^2-7a+3=0
2a-1)*(a-3)=0
2a-1=0 or a-3=0
a=1/2 or a=3
To solve the equation 2a^2 + 3 = 7a by factoring, we need to rearrange the terms so that one side of the equation equals zero.
Let's move all the terms to one side by subtracting 7a from both sides:
2a^2 - 7a + 3 = 0
Now, we need to factorize the quadratic equation. To do this, we need to find two numbers, let's call them "m" and "n", such that their coefficients add up to -7 (which is the coefficient of 'a' term) and their product is equal to the product of the coefficient of 'a^2' term and the constant term.
In this equation, the coefficient of 'a^2' term is 2 and the constant term is 3. So, we need to find two numbers, 'm' and 'n', such that:
mn = 2 * 3 = 6
m + n = -7
Let's find the factors of 6:
-1 * -6 = 6 and -1 + -6 = -7
1 * 6 = 6 and 1 + 6 = 7
-2 * -3 = 6 and -2 + -3 = -5
From these options, we see that -1 and -6 satisfy the conditions. Therefore, the factored form of the equation is:
(2a - 1)(a - 3) = 0
Now, we can solve for 'a' by setting each factor equal to zero:
(2a - 1) = 0 or (a - 3) = 0
For the first equation, add 1 to both sides and then divide by 2:
2a = 1
a = 1/2
For the second equation, add 3 to both sides:
a = 3
Therefore, the solutions to the original equation 2a^2 + 3 = 7a are a = 1/2 and a = 3.