# Algebra 2: 9x² = 25

by Ardesa
(New Smyrna Beach)

9x² = 25

Solve the following equation for all solutions of x:

9x² = 25

Check the answer by substitution the solution into the original equation

### Comments for Algebra 2: 9x² = 25

 Nov 28, 2012 Solve for x by: Staff AnswerPart I           9x² = 25To solve for x, take the square root of each side of the equation           √(9x²) = √(25)           ±3x = ±5           3x = ±5Divide each side of the equation by 3           3x / 3 = ±5 / 3           x * (3 / 3) = ±5 / 3           x * (1) = ±5 / 3           x = ±5 / 3Final Answer: x = ±5 / 3 ----------------------------------------Check the answer by substituting the two values of x into the original equationIf x = 5 / 3           9x² = 25           9(5/3)² = 25           9(5²/3²) = 25           9(25/9) = 25           25 * (9/9) = 25           25 * (1) = 25           25 = 25, OK → x = 5 / 3 is a valid solutionIf x = -5 / 3           9x² = 25           9(-5/3)² = 25           9[(-5)²/3²] = 25           9(25/9) = 25           25 * (9/9) = 25           25 * (1) = 25           25 = 25, OK → x = -5 / 3 is a valid solution ----------------------------------------

 Nov 28, 2012 Solve for x by: Staff ----------------------------------------Part IIYou can also solve this equation using the difference of squares formulaThe difference of squares formula states that:(a + b)(a - b) = a² - b²(a + b) and (a - b) are called conjugates.This idea can be applied to your problem as follows:           9x² = 25           9x² - 25 = 25 - 25           9x² - 25 = 0           (3x)² - 5² = 0Factor the left side of the equation(3x + 5)(3x - 5) = 03x - 5 = 0           3x - 5 + 5 = 0 + 5           3x + 0 = 0 + 5           3x = 5           3x / 3 = 5 / 3           x * (3 / 3) = 5 / 3           x * (1) = 5 / 3           x = 5 / 3(3x + 5)(3x - 5) = 03x + 5 = 0           3x + 5 - 5 = 0 - 5           3x + 0 = 0 - 5           3x = -5           3x / 3 = -5 / 3           x * (3 / 3) = -5 / 3           x * (1) = -5 / 3           x = -5 / 3Again, the answer is           x = ±5 / 3

 Dec 11, 2012 Solve for x by: Staff ---------------------------------------- Part III Thanks for writing. Staff www.solving-math-problems.com