Mathematics: Solve by completing the square : 4x^2-12x+7=0

Solve by completing the square : 4x^2-12x+7=0

Ответ:

XTREME3336

20.01.2022

Mathematics

$x=\frac{3}{2}\pm\frac{\sqrt{2}}{2}}$

Step-by-step explanation:

we have

4x^2-12x+7=0

step 1

Group terms that contain the same variable, and move the constant to the opposite side of the equation

4x^2-12x=-7

step 2

factor the leading coefficient

4(x^2-3x)=-7

step 3

Complete the square. Remember to balance the equation by adding the same constants to each side

4(x^2-3x+1.5^2)=-7+1.5^2(4)

4(x^2-3x+2.25)=2

simplify

(x^2-3x+2.25)=0.5

step 4

Rewrite as perfect squares

(x-1.5)^2=0.5

step 5

take square root both sides

$x-1.5=\pm\frac{1}{\sqrt{2}}$

Convert 1.5 in a fraction number

$x-\frac{3}{2}=\pm\frac{1}{\sqrt{2}}$

$x=\frac{3}{2}\pm\frac{\sqrt{2}}{2}}$

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Ответ:

coopera1744

11.08.2021

Mathematics

Divide the miles by the hours

141/3=47

205/5=41

97/2=48.5

172/4=43

97 miles in 2 hours

Step-by-step explanation:

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Solve by completing the square :

4x^2-12x+7=0

Ответ:

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