Solve the quadratic equation 25x2+35x−78=025x2+35x−78=0 by completing the square.

Sure, let's solve the quadratic equation 25x^2 + 35x - 78 = 0 by completing the square.

Step 1: Write the equation in the form of ax^2 + bx + c = 0 25x^2 + 35x - 78 = 0

Step 2: Divide the entire equation by 'a' to make the coefficient of x^2 equal to 1. x^2 + (35/25)x - 78/25 = 0 Simplify to get: x^2 + 1.4x - 3.12 = 0

Step 3: Rearrange the equation to the form x^2 + bx = c by moving the constant term to the right side of the equation. x^2 + 1.4x = 3.12

Step 4: Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation. (x + 0.7)^2 = 3.12 + 0.49 (x + 0.7)^2 = 3.61

Step 5: Take the square root of both sides of the equation. x + 0.7 = ± √3.61 x + 0.7 = ± 1.9

Step 6: Solve for x by subtracting 0.7 from both sides of the equation. x = -0.7 ± 1.9

So, the solutions are x = 1.2 and x = -2.6.