Mathematics, 30.01.2020 21:44 forschoolok123456789

Solve 5x 2 - 7x + 2 = 0 by completing the square. what are the solutions?

Answers: 2

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Answer from: coopera1744

$x=\frac{2}{5}$ or x=1

Step-by-step explanation:

The given quadratic equation is

5x^2-7x+2=0

Group the constant terms on the right hand side.

5x^2-7x=0-2

5x^2-7x=-2

Divide through by 5.

$x^2-\frac{7}{5}x=-\frac{2}{5}$

Add the square of half the coefficient of x., which is $(\frac{1}{2}\times- \frac{7}{5})^2=\frac{49}{100}$ to both sides of the equation.

$x^2-\frac{7}{5}x+\frac{49}{100}=-\frac{2}{5}+\frac{49}{100}$

The left hand side is now a perfect square.

$(x-\frac{7}{10})^2=\frac{9}{100}$

Take the square root of both sides;

$(x-\frac{7}{10})=\pm \sqrt{\frac{9}{100}}$

$x-\frac{7}{10}=\pm \frac{3}{10}$

$x=\frac{7}{10}\pm \frac{3}{10}$

$x=\frac{7-3}{10}$ or $x=\frac{7+3}{10}$

$x=\frac{4}{10}$ or $x=\frac{10}{10}$

x=1 or $x=\frac{2}{5}$

Answer from: varonadestiny1109

$x_1=1\\\\x_2=\frac{2}{5}$

Step-by-step explanation:

- You must divide the equation by 5:

$x^{2}-\frac{7}{5}x+\frac{2}{5}=0$

- Add and subtract $(\frac{\frac{7}{5}}{2})^2$ :

$x^{2}-\frac{7}{5}x+(\frac{7}{10})^2+\frac{2}{5}-(\frac{7}{10})^2=0$

Therefore, you obtain:

$(x-\frac{7}{10})^2-0.09=0$

-add 0.09} to both sides:

$(x-\frac{7}{10})^2=0.09$

- Apply square root to both sides and solve for x:

$\sqrt{(x-\frac{7}{10})^2}=\sqrt{\0.09}\\x-\frac{7}{10}=\sqrt{0.09}\\\\x_1=\frac{7}{10}+\sqrt{0.09}=1\\\\x_2=-\frac{7}{10}-\sqrt{0.09}=\frac{2}{5}$

Answer from: Quest

what graph

step-by-step explanation:

Answer from: Quest

a. we have two

lines: y = 4-x and

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b. 4-x = 8-x^-1

x 4-x 8-x^-1

-3 7

8.33

-2 6 8.5

-1 5 9

0 4

1 3

2 2

7.5

3 1 7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:

x=-4.236

y = 4-x = 4 – (-4.236)

= 8.236

y = 8-x^-1 = .236)^-1

= 8.236

x=0.236

y = 4-x = 4 – (0.236) = 3.764

y = 8-x^-1 = 8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c. to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x and y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines. the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

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