Question

When 7 times a number is added to the square of the number, the sum is 3. What is the number?​

Answer 1

`x\approx -7.405 \text{ or } x \approx 0.405`

Explanation:

1. Set up the equation

Let x = the number. Then

7x = seven times the number and

x² = the square of the number

x² + 7x = seven times the number added to the square of the number

x² + 7x = 3

Subtract 3 from each side

x² + 7x - 3 = 0

2. Solve the quadratic equation

Use the quadratic formula: a = 1; b = 7; c = -3.

`x = (-b\pm√(b^2-4ac))/(2a)\\\\=(-7\pm√((7)^2-4*1*(-3)))/(2*1)\\\\=(-7\pm√(49 + 12))/(2)\\\\=(-7\pm√(61))/(2)\\\\x = (-7 - √(61))/(2) \text{ or } x = (-7 + √(61))/(2)\\\\\mathbf{x\approx -7.405} \text{ or } \mathbf{x \approx 0.405}`

The graph of your quadratic crosses the x-axis at (-7.405,0) and (0.405,0).