sagnuhh

2021-01-24

The square of a number is added to two times the number and the sum is 24.

### Answer & Explanation

Sally Cresswell

Let he number be x.
The question is simply:
${X}^{2}+2x=24$

${X}^{2}+2x-24=0$
$\left(x-4\right)\left(x+6\right)=0$
Therefore x can be either 4 or - 6.

Vasquez

Let's assume the number as $x$. According to the problem statement, the square of the number is added to two times the number, and the sum is equal to 24. We can represent this information mathematically as:
${x}^{2}+2x=24$
To solve this equation, we can rearrange it into a quadratic equation form by subtracting 24 from both sides:
${x}^{2}+2x-24=0$
Now, we can solve this quadratic equation. To do so, we can either factorize it or use the quadratic formula. Let's use the quadratic formula to find the solutions. The quadratic formula states that for an equation of the form $a{x}^{2}+bx+c=0$, the solutions for $x$ are given by:
$x=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$
Comparing our quadratic equation to the general form, we have $a=1$, $b=2$, and $c=-24$. Substituting these values into the quadratic formula, we get:
$x=\frac{-2±\sqrt{{2}^{2}-4·1·-24}}{2·1}$
Simplifying further:
$x=\frac{-2±\sqrt{4+96}}{2}$
$x=\frac{-2±\sqrt{100}}{2}$
$x=\frac{-2±10}{2}$
Now, we can evaluate the two possible solutions:
${x}_{1}=\frac{-2+10}{2}=4$
${x}_{2}=\frac{-2-10}{2}=-6$
Hence, the two solutions for the given equation are $x=4$ and $x=-6$.

RizerMix

$x=-6$ and $x=4$
Explanation:
${x}^{2}+2x=24$
To solve this equation, we need to rearrange it into a quadratic equation form, where one side is equal to zero. Let's subtract 24 from both sides:
${x}^{2}+2x-24=0$
Now, we can factor this quadratic equation. We are looking for two numbers that multiply to -24 and add up to 2. The factors that satisfy these conditions are 6 and -4. Therefore, we can rewrite the equation as:
$\left(x+6\right)\left(x-4\right)=0$
To find the solutions, we set each factor equal to zero and solve for $x$.
Setting $x+6=0$, we have:
$x=-6$
Setting $x-4=0$, we have:
$x=4$
Therefore, the solutions to the equation are $x=-6$ and $x=4$.

user_27qwe

To solve the given problem, let's assume the number as $x$. According to the problem statement, we have the equation:
${x}^{2}+2x=24$
To solve this quadratic equation, we need to rearrange it into the standard form:
${x}^{2}+2x-24=0$
Now, we can solve this quadratic equation using factoring or the quadratic formula. Let's solve it using factoring:
$\left(x-4\right)\left(x+6\right)=0$
Setting each factor equal to zero, we have:
$x-4=0\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}x+6=0$
Solving these equations, we find:
$x=4\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}x=-6$
Therefore, the possible solutions for the given equation are $x=4$ or $x=-6$.

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