Solve by completing the square. $\newline$ $r^2 + 26r = -29$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $r =$ _ or $r =$ _

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

r^2 + 26r = -29

\newline

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

\newline

r =

_____ or

r =

_____

Write Equation Form: Write the equation in the form of $r^2 + br = c$ . We have the equation $r^2 + 26r = -29$ .
Move Constant Term: Move the constant term to the right side of the equation. $\newline$ Add $29$ to both sides to isolate the $r$ terms on the left. $\newline$ $r^2 + 26r + 29 = 0$
Find Completing Number: Find the number to complete the square. $\newline$ Take half of the coefficient of $r$ , which is $26$ , and square it. $(26/2)^2 = 13^2 = 169$ .
Add/Subtract Completing Number: Add and subtract the number found in Step $3$ to the left side of the equation. $\newline$ $r^2 + 26r + 169 - 169 = 29$
Factor Perfect Square Trinomial: Factor the perfect square trinomial on the left side of the equation. $\newline$ $(r + 13)^2 - 169 = 29$
Move Constant Term Right: Move the constant term to the right side to set up for taking the square root. $\newline$ $(r + 13)^2 = 29 + 169$ $\newline$ $(r + 13)^2 = 198$
Take Square Root: Take the square root of both sides of the equation. $\newline$ $\sqrt{(r + 13)^2} = \pm\sqrt{198}$ $\newline$ $r + 13 = \pm\sqrt{198}$
Solve for r: Solve for r by subtracting $13$ from both sides. $r = -13 \pm \sqrt{198}$
Simplify Square Root: Simplify the square root and round to the nearest hundredth if necessary. $\newline$ $\sqrt{198} \approx 14.07$ $\newline$ $r = -13 \pm 14.07$
Find Two Values: Find the two values of $r$ . $r \approx -13 + 14.07$ implies $r \approx 1.07$ . $r \approx -13 - 14.07$ implies $r \approx -27.07$ .Values of $r$ : $1.07$ , $-27.07$