How to Solve Linear Equations With a Square Root

Linear equations can be solved as long as a constant term is under the square root.

Linear equations are algebraic equations where each term (or number) is either constant or dependent on the product of a single unknown variable. Linear equations can generally be described by the equation y = m*x + b where the variable "x" is an unknown quantity which must be determined. While the variable "x" cannot be under a square root by the definition of a linear equation (which states that x is a first power term), the constant terms may be under a square root. These equations are straightforward to solve.

Instructions

1. Isolate the terms that contain the variable "x." For example, if the equation given is sqrt(9) = 4*x -5 (where "sqrt(9)" means 9 is under the square root sign and "*" means multiplication), then add the number 5 to both sides of the equation. This will give the new equation sqrt(9) + 5 = 4*x.

2. Simplify the left-hand side of the equation. In this example, the square root of 9 is 3, so adding 3 and 5 on the left-hand side of the equation gives 8 = 4*x.

3. Isolate "x" by dividing the number in front of "x" by the numbers on both sides of the equation. In this example, dividing 8 by 4 gives 2, and dividing 4*x by 4 gives 1*x, which can be simplified to just x. The equation is now x = 2. Therefore, the variable "x" is actually the number 2, and the equation is solved.

References

• SOS Math: Solving Equations