Question

How do you solve $5{x^2} - 3x + 7 = 7$ by factoring ?

Answer 1

Hint: The given problem requires us to solve an equation. There are various methods that can be employed to solve a quadratic equation like completing the square method, using a quadratic formula and by splitting the middle term but we are required to solve the equation using simple factorization.

Complete step by step solution:
In the given question, we are required to solve the equation $5{x^2} - 3x + 7 = 7$ .
Quadratic equations can be solved by various methods like splitting the middle term, using the quadratic formula, factoring the common factor, and completing the square method.
We can solve the given equation by any of the methods.
Consider the equation $5{x^2} - 3x + 7 = 7$.
The equation can be factorized easily as x can be taken out common from both the terms in the equation.
So, $5{x^2} - 3x + 7 = 7$
Shifting all the constant terms to the right side of the equation, we get,
$ \Rightarrow 5{x^2} - 3x = 7 - 7$
Cancelling out the like constant terms with opposite signs,
$ \Rightarrow 5{x^2} - 3x = 0$
Taking x common from both the terms, we get,
$ \Rightarrow x\left( {5x - 3} \right) = 0$
Now, either $x = 0$ or $\left( {5x - 3} \right) = 0$.
Either $x = 0$ or $x = \left( {\dfrac{3}{5}} \right)$ .
So, the roots of the given equation $5{x^2} - 3x + 7 = 7$ are: $x = 0$ and $x = \left( {\dfrac{3}{5}} \right)$

Note: Quadratic equations are the polynomial equations with degree of the variable. Quadratic formula is the easiest and most efficient formula to calculate the roots of an equation. Quadratic equations can also be solved by splitting the middle term and completing the square method. Quadratic equations may also be solved by hit and trial method if the roots of the equation are easy to find.