Question

The square of a number 60 greater than half of the number. Form a
quadratic equation and solve to determine the possible values of the
number.

Answer 1

Answer:

The number could be $-7.5$ or $8$.

Step-by-step explanation:

I'm going to assume this means "The square of a number is 60 greater than half of the number." Let the number be $x$. The square of $x$ will be $x^{2}$. "is" denotes that we use the "$=$" sign, so our equation so far is $x^{2} =$ . Half of $x$ is $\frac{1}{2}x$, and "greater than" implies addition, so $60$ greater than $\frac{1}{2}x$ is $\frac{1}{2}x+60$. Therefore, the equation is $x^{2} =\frac{1}{2}x+60$.

Solving for $x$, we get:

$x^{2} =\frac{1}{2}x+60$

$2x^{2} =x+120$ (Multiply both sides of the equation by $2$ to get rid of the fraction)

$2x^{2} -x-120=0$ (Subtract $x+120$ from both sides of the equation to make it easier to solve)

$2x^{2} +15x-16x-120=0$ (Split $-x$ into $15x-16x$ to make the LHS easier to factor)

$x(2x+15)-8(2x+15)=0$ (Take a common factor out of the first two terms and the last two terms)

$(2x+15)(x-8)=0$ (Take another common factor out)

$2x+15=0,x-8=0$ (Zero Product Property)

$x=-7.5,8$ (Solve)

Hope this helps!