Solve the quadratic equation by the square root property
(2x - 1)2 = 25
To solve the quadratic equation (2x - 1)² = 25 using the square root property, we need to isolate the squared term and then take the square root of both sides. Here's how you can do it step-by-step:
Step 1: Expand the squared term on the left side of the equation.
(2x - 1)² = 25
4x² - 4x + 1 = 25
Step 2: Move the constant term to the other side of the equation.
4x² - 4x + 1 - 25 = 0
4x² - 4x - 24 = 0
Step 3: Divide the entire equation by the coefficient of the x² term to simplify the equation.
4(x² - x - 6) = 0
Step 4: Factor the quadratic expression inside the parentheses, if possible.
(x - 3)(x + 2) = 0
Step 5: Set each factor equal to zero and solve for x.
x - 3 = 0 or x + 2 = 0
Step 6: Solve for x in each equation.
x = 3 or x = -2
Therefore, the solutions to the quadratic equation (2x - 1)² = 25 are x = 3 or x = -2.
To solve the quadratic equation using the square root property, we first need to isolate the squared term on one side of the equation. Let's start by expanding the expression (2x - 1)²:
(2x - 1)² = 25
4x² - 4x + 1 = 25
Next, we'll move the constant term to the other side of the equation:
4x² - 4x + 1 - 25 = 0
4x² - 4x - 24 = 0
Now, the equation is in the form ax² + bx + c = 0, where a = 4, b = -4, and c = -24. We can solve this quadratic equation using the square root property.
The square root property states that if ax² + bx + c = 0, then x = (-b ± √(b² - 4ac)) / 2a.
Applying this formula to our equation, we have:
x = (-(-4) ± √((-4)² - 4 * 4 * -24)) / (2 * 4)
x = (4 ± √(16 + 384)) / 8
x = (4 ± √400) / 8
x = (4 ± 20) / 8
This gives us two possible solutions:
x₁ = (4 + 20) / 8 = 24 / 8 = 3
x₂ = (4 - 20) / 8 = -16 / 8 = -2
Hence, the solutions to the equation (2x - 1)² = 25 are x = 3 and x = -2.
( 2 x - 1 ) ^ 2 = 25
Take the square root of both sidea
2 x - 1 = + OR - 5
Add 1 to both sides
2 x - 1 + 1 = + OR - 5 + 1
2 x = + OR - 5 + 1
Divide both sides by 2
x = ( + OR - 5 + 1 ) / 2
x 1 = ( 5 + 1 ) / 2 = 6 / 2 = 3
x 2 = ( - 5 + 1 ) / 2 = - 4 / 2 = - 2