Chapter Closure
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You can solve for the variable by using cross products.
Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.
Make sure you write all the terms on the left-hand side of the equation and simplify as much as possible before using the Quadratic Formula.
x≈3.39
x=1/3
x=3 and x=-6
To solve the proportion, we will start by using cross products. Remember that we will need to treat x+2 and 10-2x as single quantities in the cross multiplication process.
From here, we will continue solving for x by using the Distributive Property and the Properties of Equality.
To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side, using the Properties of Equality.
Now we can continue to isolate x using the Multiplication and Division Properties of Equality.
LHS * x=RHS* x
x * a/x= a
.LHS /9.=.RHS /9.
a/b=.a /9./.b /9.
a/1=a
a/b=.a /3./.b /3.
Rearrange equation
We will use the Quadratic Formula to solve the given quadratic equation.
ax^2+ bx+ c=0 ⇔ x=- b± sqrt(b^2-4 a c)/2 a
Let's start by rewriting the equation so all of the terms are on the left-hand side and then simplify as much as possible.
Now, we can identify the values of a, b, and c. x^2+3x-18=0 ⇔ 1x^2+ 3x+( -18)=0 We see that a= 1, b= 3, and c= - 18. Let's substitute these values into the Quadratic Formula.
Substitute values
Calculate power
a * 1=a
- a(- b)=a* b
Add terms
Calculate root
The solutions for this equation are x= -3± 92. Let's separate them into the positive and negative cases.
| x=-3± 9/2 | |
|---|---|
| x_1=-3+9/2 | x_2=-3-9/2 |
| x_1=6/2 | x_2=-12/2 |
| x_1=3 | x_2=-6 |
Using the Quadratic Formula, we found that the solutions of the given equation are x_1=3 and x_2=-6.