Respuesta :
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation h*(x)-(x^2+3*x-18)=0
Step-by-step explanation:
Equation at the end of step 1 :
hx - x2 - 3x + 18 = 0
Step 2 :
Solving a Single Variable Equation :
2.1 Solve hx-x2-3x+18 = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
This function is h(x) = (x+ 6)(x-3)
What is a function?
An expression which defines the relationship between two variables (one independent and one dependent variable).
What is dependent and independent variable?
The independent variable is the variable being controlled in the problem, and the dependent variable is the variable that changes with the change of independent variable.
What is a quadratic function?
A function whose highest degree is 2 is called a quadratic function.
What is completing the square method ?
Rewriting the function in the form of a squared bracket and then adding constant if necessary is called the completing the square method.
How to rewrite the function by completing the square?
The given function is
[tex]h(x) = x^{2} + 3x - 18[/tex]
- Here we should try to make it in the form of [tex]a^{2} + 2ab + b^{2}[/tex].
We can write,
[tex]h(x) = x^{2} + 2x(\frac{3}{2} ) + (\frac{3}{2} )^{2} - (\frac{3}{2} )^{2} -18[/tex]
⇒ [tex]h(x) = (x + \frac{3}{2} )^{2} -(18 + \frac{9}{4} )[/tex]
⇒ [tex]h(x) = (x + \frac{3}{2} )^{2} -( \frac{81}{4} )[/tex]
⇒ [tex]h(x) = (x + \frac{3}{2} )^{2} -( \frac{9}{2} )^{2}[/tex]
This is the completing the square method.
- h(x) is in the form of a² - b².
- We know that a² - b² = (a+b)(a-b)
∴ [tex]h(x) = (x + \frac{3}{2} + \frac{9}{2} )(x + \frac{3}{2} - \frac{9}{2} )[/tex]
⇒ [tex]h(x) = (x + 6 )(x - 3)[/tex]
So, the given function can be written as [tex]h(x) = (x + 6 )(x - 3)[/tex]
Find out more about 'Completing the square method' here:
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