Michael Maggard

2021-12-27

To solve:

${x}^{2}+11x+24=0$

Deufemiak7

Beginner2021-12-28Added 34 answers

Step 1

Given:

Split the middle term 11x as

Replace 11x with

The above equation can be written ads

Apply distributive property for first two terms and last two terms,

Again apply distributive property for

So the factors are

To find the value of x

Take

Subtract 8 on both sides,

Take

Subtract 3 on both sides,

So, the values of x are -8 and -3

Vivian Soares

Beginner2021-12-29Added 36 answers

Step 1

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form

${x}^{2}+bx=c$

${x}^{2}+11x+24=0$

Subtract 24 from both sides of the equation.

${x}^{2}+11x+24-24=-24$

Subtracting 24 from itself leaves 0

${x}^{2}+11x=-24$

Divide 11, the coefficient of the x term, by 2 to get$\frac{11}{2}$ . Then add the square of $\frac{11}{2}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$x}^{2}+11x+{\left(\frac{11}{2}\right)}^{2}=-24+{\left(\frac{11}{2}\right)}^{2$

Square$\frac{11}{2}$ by squaring both the numerator and the denominator of the fraction.

$x}^{2}+11x+\frac{121}{4}=-24+\frac{121}{4$

Add -24 to$\frac{121}{4}$

$x}^{2}+11x+\frac{121}{4}=\frac{25}{4$

Factor$x}^{2}+11x+\frac{121}{4$ . In general, when ${x}^{2}+bx+c$ is a perfect square, it can always be factored as $(x+\frac{b}{2})}^{2$

$(x+\frac{11}{2})}^{2}=\frac{25}{4$

Take the square root of both sides of the equation.

$\sqrt{{(x+\frac{11}{2})}^{2}}=\sqrt{\frac{25}{4}}$

Simplify.

$x+\frac{11}{2}=\frac{5}{2}$

$x+\frac{11}{2}=-\frac{5}{2}$

Subtract$\frac{11}{2}$ from both sides of the equation.

$x=-3$

$x=-8$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form

Subtract 24 from both sides of the equation.

Subtracting 24 from itself leaves 0

Divide 11, the coefficient of the x term, by 2 to get

Square

Add -24 to

Factor

Take the square root of both sides of the equation.

Simplify.

Subtract

karton

Expert2022-01-09Added 613 answers

Step 1

Determine the quadratic equation's coefficients a, b and c

Use the standard form,

a=1

b=11

c=24

Step 2

Plug these coefficients into the quadratic formula

The quadratic formula gives us the roots for

b=11

c=24

Simplify exponents and square roots

to get the result:

Step 3

Simplify square root

Simplify 25 by finding its prime factors

The prime factorization of 25 is

Write the prime factors:

Group the prime factors into pairs and rewrite them in exponent form:

Use the rule

Step 4

Solve the equation for x

The

Separate the equations:

Find the volume V of the described solid S

A cap of a sphere with radius r and height h.

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?

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