Solve 𝑥 squared plus two is equal to 100.01.
In order to solve any equation, we need to calculate the value or values of 𝑥 that mean that the left-hand side is equal to the right-hand side. When dealing with a quadratic equation, one where the highest power of 𝑥 is two, we usually end up with two answers or two solutions. Let’s consider the equation we were given in this question: 𝑥 squared plus two is equal to 100.01.
In order to work out the value or values of 𝑥, we firstly need to subtract two from both sides of the equation. Two minus two is equal to zero. Therefore, the left-hand side becomes 𝑥 squared. 100.01 minus two is equal to 98.01. Therefore, 𝑥 squared is equal to 98.01. In order to work out 𝑥, we now need to square root both sides of the equation as square rooting is the opposite or inverse operation of squaring. The square root of 𝑥 squared is equal to 𝑥. On the right-hand side, we have the square root of 98.01. When square rooting a number, we need to remember that we have two possible solutions: the positive square root and the negative square root. Typing the square root of 98.01 into our calculator gives us an answer of 9.9. This means that 𝑥 equals positive or negative 9.9.
There are two solutions to the equation 𝑥 squared plus two equals 100.01. They are 𝑥 equals 9.9 and 𝑥 equals negative 9.9. We can check these solutions by substituting them back into the initial equation. Firstly, we will substitute 𝑥 equals 9.9. This gives us 9.9 squared plus two. 9.9 squared is equal to 98.01. Adding two to this gives us an answer of 100.01. So our first solution is definitely correct.
Secondly, we need to substitute 𝑥 equals negative 9.9. This gives us negative 9.9 squared plus two. Squaring a number means multiplying it by itself. And multiplying a negative number by another negative number gives us a positive number. This means that negative 9.9 squared is also equal to 98.01. Adding two to this gives us 100.01. Therefore, the answer 𝑥 equals negative 9.9 is also correct.