Order the steps for solving x²-14x=15 by completing the square.
1. Move the constant term to the right side of the equation: x² - 14x = 15 becomes x² - 14x - 15 = 0.
2. Take half of the coefficient of x (which is -14) and square it: (-14/2)² = 49.
3. Add the square from step 2 to both sides of the equation: x² - 14x + 49 = 15 + 49.
4. Rewrite the left side as a perfect square: (x - 7)² = 64.
5. Take the square root of both sides of the equation: x - 7 = ±√64.
6. Solve for x by adding 7 to both sides and simplifying: x = 7 ± 8.
7. Thus, the solutions to the equation x² - 14x = 15 are x = 15 and x = -1.
just solve the equation and SHOW me the steps
Sure! Here are the steps for solving x² - 14x = 15 by completing the square:
1. Move the constant term to the right side of the equation: x² - 14x = 15
2. Add the square of half the coefficient of x to both sides: x² - 14x + (-7)² = 15 + (-7)²
3. Simplify the equation: x² - 14x + 49 = 64
4. Rewrite the left side as a perfect square: (x - 7)² = 64
5. Take the square root of both sides: x - 7 = ±√64
6. Solve for x: x = 7 ± 8
Therefore, the solutions to the equation x² - 14x = 15 are:
x = 7 + 8 = 15
x = 7 - 8 = -1