Introduction:
Complete squaring is an application of algebra . this means the given equation is having solution, it means each equation is having one or more solutions. now a days technology is also uses in mathematics and the students is learning in online. the tutors would explain step by step for the students.
In this content we learned about the complete square problems. I like to share this Types of Triangle with you all through my article.
Complete Square Method Problems:
Example:
Solve the equation for x x^2 + 8x + 15 = 0
Solution:
There are three terms in this equation. One is constant (15) and the others contain variables (x^2 and 8x).
in this problem we do factor the equation by determining what two numbers multiplied together gives a result of 15 when added give a sum of 8.
The factored equation looks like this:
(x + 3)(x + 5) = 0 (a)
the rule is First, Outside, Inside, Last (FOIL) method,
x^2 + 5x + 3x + 15 = 0 ----> x^2 + 8x + 15 = 0 (b)
We convert equation (a) into its terms and set each term equal to zero:
(x + 3) = 0 (c)
(x + 5) = 0 (d)
Now, solve each for x:
x + 3 = 0
subtract 3 from each side
x = -3
x + 5 = 0
subtract 5 from each side
x = -5
solutions are that x is equal to -3 or -5.
substitute x values in equation( 1 )
start with -3:
(-3)^2 + 8(-3) +15 = 0
(9) + (-24) + 15 = 0 This is a true statement so -3 is a solution.
Next, -5:
(-5)^2 + 8(-5) + 15 = 0
(25) + (-40) + 15 =0 This is also a true statement so -5 is a solution.
So answer is x = -3
and x = -5
Example2:Solve the equation for 2x^2 - 3x + 1 = 0
Solution:
2x^2 - 3x + 1 = 0
2x^2 - 3x = -1
x^2 - (3/2)x = -1/2
2a = 3/2
a = 3/4
a^2 = 9/16, so we add 9/16 to both sides:
x^2 - (3/2)x + 9/16 = -1/2 + 9/16 = 1/16
(x - 3/4)^2 = 1/16
x - 3/4 = +/- 1/4
x = 3/4 +/- 1/4
x = 1, 1/2
Understanding hard math problems for 4th graders is always challenging for me but thanks to all math help websites to help me out.
Practice Problems:
Solve the equations for competing square
1)x^2 - x - 1 = 0
2)x^2-6x=16
Complete squaring is an application of algebra . this means the given equation is having solution, it means each equation is having one or more solutions. now a days technology is also uses in mathematics and the students is learning in online. the tutors would explain step by step for the students.
In this content we learned about the complete square problems. I like to share this Types of Triangle with you all through my article.
Complete Square Method Problems:
Example:
Solve the equation for x x^2 + 8x + 15 = 0
Solution:
There are three terms in this equation. One is constant (15) and the others contain variables (x^2 and 8x).
in this problem we do factor the equation by determining what two numbers multiplied together gives a result of 15 when added give a sum of 8.
The factored equation looks like this:
(x + 3)(x + 5) = 0 (a)
the rule is First, Outside, Inside, Last (FOIL) method,
x^2 + 5x + 3x + 15 = 0 ----> x^2 + 8x + 15 = 0 (b)
We convert equation (a) into its terms and set each term equal to zero:
(x + 3) = 0 (c)
(x + 5) = 0 (d)
Now, solve each for x:
x + 3 = 0
subtract 3 from each side
x = -3
x + 5 = 0
subtract 5 from each side
x = -5
solutions are that x is equal to -3 or -5.
substitute x values in equation( 1 )
start with -3:
(-3)^2 + 8(-3) +15 = 0
(9) + (-24) + 15 = 0 This is a true statement so -3 is a solution.
Next, -5:
(-5)^2 + 8(-5) + 15 = 0
(25) + (-40) + 15 =0 This is also a true statement so -5 is a solution.
So answer is x = -3
and x = -5
Example2:Solve the equation for 2x^2 - 3x + 1 = 0
Solution:
2x^2 - 3x + 1 = 0
2x^2 - 3x = -1
x^2 - (3/2)x = -1/2
2a = 3/2
a = 3/4
a^2 = 9/16, so we add 9/16 to both sides:
x^2 - (3/2)x + 9/16 = -1/2 + 9/16 = 1/16
(x - 3/4)^2 = 1/16
x - 3/4 = +/- 1/4
x = 3/4 +/- 1/4
x = 1, 1/2
Understanding hard math problems for 4th graders is always challenging for me but thanks to all math help websites to help me out.
Practice Problems:
Solve the equations for competing square
1)x^2 - x - 1 = 0
2)x^2-6x=16
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