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By root, I'm going to assume you mean a square root.
First, you try to isolate the root.
Then, you simplify
Then, you square everything (EVERYTHING).
Set everything equal to zero.
Then, you can solve for x using factoring.
EX)
√3x+2x+4=3x-2
Isolate your x. Therefore,
√3x+2x=3x-2-4
√3x=3x-2x-2-4
Simplify.
√3x=x-6
Square everything.
(√3x)²=x²-6²
Then, you get 3x=x²-36
Set it all = to zero.
x²-3x-36=0
Now, you can factor. Factoring is a whole nother topic, it can be found on any website. Just Google search "factoring". For this problem, you're gonna have to use the quadratic formula. Rather than do all that, I'm just going to say your answers-
x=7.68465
x=-4.6846
You (normally) will have two answers when solving a sq rt problem, because in the last step, you end up with an (x+/-#)times(x+/-#)=0. You then set both of these parentheses equal to zero, so you have two answers.
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What does it mean when the result of solving a linear equation is x equals 0?
Solving a one variable linear equation involves getting the variable on one side of the equals sign by itself. To do this one uses the properties of numbers.
How would solving a literal equation differ from a one or two step equation?
The difference is that first you have to understand the problem and translate it into an equation (or equations).
How is solving a two step equation different from one step equations?
In a two step equation, you need to do another step.
How is equality maintained when solving an equation?
Whatever is done on one side of the equation must be repeated on the other side of the equation to maintain balance and equality.
What method is used for solving a rational equation?
Methods vary considerably depending upon the number of powers in the equation. For example, the method for solving cubics is quite different to solving quadratics etc... It's not really possible to generalise to one technique.
How is solving a two step equation like solving one step equation?
the alikes of solving a one-step or two-step equation: in solving an equation is to have only variables on one side of the equal sign and numbers on the other side of the equal sign. The other alike is to have the number in front of the variable equal to one the variable does not always have to be x. These equations can use any letter as a variable.
Is satisfying an equation the same as solving it?
No. If an equation has many solutions, any one of them will satisfy it.
How does solving a literal equation differ from solving a linear equation?
Because linear equations are based on algebra equal to each other whereas literal equations are based on solving for one variable.
What does it mean when the result of solving a linear equation is x equals 0?
Solving a one variable linear equation involves getting the variable on one side of the equals sign by itself. To do this one uses the properties of numbers.
If the discriminant of a quadratic equation is zero and one root of the equation is 5 what is the value of the other root?
It too will have a value of 5
How would solving a literal equation differ from a one or two step equation?
The difference is that first you have to understand the problem and translate it into an equation (or equations).
What is a radical equation?
A radical equation is an equation that contains a variable inside a radical, such as a square root or a cube root. Solving radical equations involves isolating the radical term and then squaring both sides of the equation to eliminate the radical. It is important to check for extraneous solutions when solving radical equations.
What is the goal of solving an equation with one variable?
The goal is to find what value or values the variable may have, to make the equation true.
How is solving a two step equation different from one step equations?
In a two step equation, you need to do another step.
How is equality maintained when solving an equation?
Whatever is done on one side of the equation must be repeated on the other side of the equation to maintain balance and equality.
What method is used for solving a rational equation?
Methods vary considerably depending upon the number of powers in the equation. For example, the method for solving cubics is quite different to solving quadratics etc... It's not really possible to generalise to one technique.
When solving an equation do we need to keep the value of any one side of the equation unchanged?
No. Whatever you do to one side, you must also do to the other side.
