Solve by completing the square. $\newline$ $d^2 - 20d - 47 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $d =$ _ or $d =$ _

View step-by-step help

Home

Math Problems

Algebra 2

Solve a quadratic equation by completing the square

Full solution

Q. Solve by completing the square.

\newline

d^2 - 20d - 47 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

d =

_____ or

d =

_____

Rewrite in standard form: $d^2 - 20d - 47 = 0$ $\newline$ Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ Add $47$ to both sides. $\newline$ $d^2 - 20d - 47 + 47 = 0 + 47$ $\newline$ $d^2 - 20d = 47$
Complete the square: $d^2 - 20d = 47$ $\newline$ Choose the number to add to both sides to complete the square. $\newline$ Since $(-20/2)^2 = 100$ , add $100$ to both sides. $\newline$ $d^2 - 20d + 100 = 47 + 100$ $\newline$ $d^2 - 20d + 100 = 147$
Identify factored form: $d^2 - 20d + 100 = 147$ $\newline$ Identify the equation after factoring the left side. $\newline$ $d^2 - 20d + 100 = 147$ $\newline$ $(d - 10)^2 = 147$
Take square root: $(d − 10)^2 = 147$ $\newline$ Identify the equation after taking the square root on both sides. $\newline$ Take the square root of both sides of the equation. $\newline$ $\sqrt{(d − 10)^2} = \sqrt{147}$ $\newline$ d − $10$ = $\pm\sqrt{147}$
Isolate variable: We found: $\newline$ $d - 10 = \pm\sqrt{147}$ $\newline$ Choose the equation after isolating the variable $d$ . $\newline$ To isolate $d$ , add $10$ to both sides of the equation. $\newline$ $d - 10 + 10 = \pm\sqrt{147} + 10$ $\newline$ $d = 10 \pm \sqrt{147}$
Isolate variable: We found: $\newline$ $d - 10 = \pm\sqrt{147}$ $\newline$ Choose the equation after isolating the variable $d$ . $\newline$ To isolate $d$ , add $10$ to both sides of the equation. $\newline$ $d - 10 + 10 = \pm\sqrt{147} + 10$ $\newline$ $d = 10 \pm \sqrt{147}$ We have: $\newline$ $d = 10 \pm \sqrt{147}$ $\newline$ What are the two values of $d$ ? $\newline$ $d = 10 + \sqrt{147}$ implies $d \approx 10 + 12.12$ which is $d$ $0$ . $\newline$ $d$ $1$ implies $d$ $2$ which is $d$ $3$ . $\newline$ Values of $d$ : $d$ $5$ , $d$ $6$