Solve by completing the square. f^2 − 14f = 31 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. f = _____ or f = _____

Question

Solve by completing the square.  f^2 − 14f = 31 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.  f = _____ or f = _____

Bytelearn · Accepted Answer

Write Equation Form: Write the equation in the form of f^2 + bf = c. The given equation is already in this form: f^2 − 14f = 31.Move Constant Term: Move the constant term to the right side of the equation. Add 31 to both sides to isolate the f^2 and f terms on one side. f^2 − 14f + 31 - 31 = 31 + 31 f^2 − 14f = 31Find Completion Number: Find the number to complete the square. Take half of the coefficient of f, square it, and add it to both sides of the equation. (-14/2)^2 = 49 f^2 − 14f + 49 = 31 + 49 f^2 − 14f + 49 = 80Factor Left Side: Factor the left side of the equation. The left side is now a perfect square trinomial. (f − 7)^2 = 80Take Square Root: Take the square root of both sides of the equation. Remember to consider both the positive and negative square roots. √((f − 7)^2) = ±√80 f − 7 = ±√80Solve for f: Solve for f by isolating the variable. Add 7 to both sides of the equation to get f by itself. f − 7 + 7 = ±√80 + 7 f = 7 ±√80Simplify Square Root: Simplify the square root and round to the nearest hundredth if necessary. √80 is approximately 8.94 when rounded to the nearest hundredth. f = 7 ± 8.94Find Values of f: Find the two values of f. f = 7 + 8.94 implies f ≈ 15.94. f = 7 - 8.94 implies f ≈ -1.94. Values of f: 15.94, -1.94

Solve by completing the square. $\newline$ $f^2 - 14f = 31$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $f =$ _ or $f =$ _

Full solution

More problems from Solve a quadratic equation by completing the square

Related topics

Solve by completing the square.\newlinef2−14f=31f^2 - 14f = 31f2−14f=31\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinef=f = f= _____ or f=f = f= _____

Solve by completing the square. $\newline$ $f^2 - 14f = 31$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $f =$ _ or $f =$ _