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2 years ago

Solve 5x^2+2x=1 using either factoring, square root method, completing the square or quadratic formula.

Mathematics

1 answer:

wolverine [178]2 years ago

4 0

Answer:

x = -1 ± √6 / 5

Step-by-step explanation:

Solve $5x^{2}$ + 2x = 1

move 1 to the left side of the equation by subtracting it from both sides.

$5x^{2}$ + 2x - 1 = 0

Use the quadratic formula to find the solutions.

-b± $\sqrt{b^2 - 4 (ac)}$ / 2a

Substitute the values a = 5 , b = 2, and c = -1 into the quadratic formula and solve for x

-2± $\sqrt{2^2 - 4(5 - 1)}$ / 2 ⋅ 5

Simplify.

x = -2 ± 2 $\sqrt{6}$ / 10

x = -1 ± $\sqrt{6}$ / 5

Exact Form:

x = -1 ± $\sqrt{6}$ / 5

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2 years ago

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2 years ago

What are the exact solutions of x2 − 5x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 ti

Marat540 [252]

Answer:

$x = \frac{5 + \sqrt{53}}{2}$ or $x = \frac{5 - \sqrt{53}}{2}$

Step-by-step explanation:

Given

$x^2 - 5x - 7 = 0$

Required

Solve for x using:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

First, we need to identify a, b and c

The general form of a quadratic equation is:

$ax^2 + bx + c = 0$

So, by comparison with $x^2 - 5x - 7 = 0$

$a = 1$ $b = -5$ $c = -7$

Substitute these values of a, b and c in

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-5) \± \sqrt{(-5)^2 - 4 * 1 * -7}}{2 * 1}$

$x = \frac{5 \± \sqrt{25 +28}}{2}$

$x = \frac{5 \± \sqrt{53}}{2}$

Split the expression to two

$x = \frac{5 + \sqrt{53}}{2}$ or $x = \frac{5 - \sqrt{53}}{2}$

To solve further in decimal form, we have

$x = \frac{5 + 7.28}{2}$ or $x = \frac{5 - 7.28}{2}$

$x = \frac{12.28}{2}$ or $x = \frac{-2.28}{2}$

$x = 6.14$ or $x = -1.14$

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2 years ago

Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped with side lengths of 9 inches, and t

MatroZZZ [7]

To solve this problem, you must follow the proccedure below:

1. The block was cube-shaped with side lengths of 9 inches and to calculate its volume (V1), you must apply the following formula:

V1=s³

s is the side of the cube (s=9)

2. Therefore, you have:

V1=s³
V1=(9 inches)³
V1=729 inches³

3. The lengths of the sides of the hole is 3 inches. Therefore, you must calculate its volume (V2) by applying the formula for calculate the volume of a rectangular prism:

V2=LxWxH

L is the length (L=3 inches).
W is the width (W=3 inches).
H is the heigth (H=9 inches).

4. Therefore, you have:

V2=(3 inches)(3 inches)(9 inches)
V2=81 inches

5. The amount of wood that was left after the hole was cut out, is:

Vt=V1-V2
Vt=648 inches³

7 0

2 years ago