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How do you Solve 7x^2+3x-4=0?

TopQuadratic equations in Math can be solved using mid - term splitting technique. This method may not always be true for all equations. In mid – term splitting, the coefficient of term which has degree 1 of x is split on basis of calculation of product of coefficients of terms involving x2 and x0. So, let us understand how this approach works for quadratic equations through an example:

Example: How do you solve 7x to the power 2 plus 3x minus 4 equal to 0?

Solution: Quadratic equation that has been given to us is of the form:
7x2 + 3x – 4 = 0,
When this equation is compared to general equation of a Quadratic Equation i.e. Ax2 + B x + C = 0, we see that:
A = 7,
B = 3 and,
C = - 4,
On multiplying A and C we get 7 * -4 = - 28.

Now to use mid - term splitting technique we first check for two Numbers such that their product is -28 and their difference or addition is 3. We see that 7 and – 4 would result into respective product and difference. So, we can split middle term as follows:
7 x2 + 3x – 4 = 0,
7 x2 + 7x – 4x – 4 = 0,
Factorizing the above equation:
7x (x + 1) – 4 (x + 1) = 0,
Or (x + 1) (7 x – 4) = 0,
Or x + 1 = 0 and 7x – 4 = 0,
Or x = - 1 and x = 4 /7,

Thus we get two roots for equation as x = - 1 and x = 4 /7.