Answer:
[tex]\frac{9}{4}[/tex]
Step-by-step explanation:
Given
x² + 3x - 13 = 0 ( add 13 to both sides )
x² + 3x = 13
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2([tex]\frac{3}{2}[/tex] )x + ([tex]\frac{3}{2}[/tex] )² = 13 + ([tex]\frac{3}{2}[/tex] )², that is
x² + 2([tex]\frac{3}{2}[/tex] )x + [tex]\frac{9}{4}[/tex] = 13 + [tex]\frac{9}{4}[/tex]
(x + [tex]\frac{3}{2}[/tex] )² = [tex]\frac{61}{4}[/tex]
The required number to be added to complete the square is [tex]\frac{9}{4}[/tex]
Hence, required number to be added to complete the square is 9/4
A quadratic equation is any equation that can be rewritten in standard form as ax2+bx+c=0 in algebra. When x is an unknown and a, b, and c are known numbers, and an is less than 0. Because there is no ax2 term when a = 0, the equation is linear rather than quadratic.
Given equation =x² + 3x - 13 = 0 ( add 13 to both sides )
=x² + 3x = 13
using complete the square and add ( half the coefficient of the x- term )² to both sides
=x² + 2(3/2 )x + ( 3/2)² = 13 + (3/2 )², that is
=x² + 2(3/2 )x + = 13 + 9/4
=(x + 3/2 )² = 61/4
The required number to be added to complete the square is 9/4
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