16x^2-24x-25=0

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Solution for 16x^2-24x-25=0 equation:


Simplifying
16x2 + -24x + -25 = 0

Reorder the terms:
-25 + -24x + 16x2 = 0

Solving
-25 + -24x + 16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
-1.5625 + -1.5x + x2 = 0

Move the constant term to the right:

Add '1.5625' to each side of the equation.
-1.5625 + -1.5x + 1.5625 + x2 = 0 + 1.5625

Reorder the terms:
-1.5625 + 1.5625 + -1.5x + x2 = 0 + 1.5625

Combine like terms: -1.5625 + 1.5625 = 0.0000
0.0000 + -1.5x + x2 = 0 + 1.5625
-1.5x + x2 = 0 + 1.5625

Combine like terms: 0 + 1.5625 = 1.5625
-1.5x + x2 = 1.5625

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 1.5625 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 1.5625 + 0.5625

Combine like terms: 1.5625 + 0.5625 = 2.125
0.5625 + -1.5x + x2 = 2.125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 2.125

Calculate the square root of the right side: 1.457737974

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.457737974 and -1.457737974.

Subproblem 1

x + -0.75 = 1.457737974 Simplifying x + -0.75 = 1.457737974 Reorder the terms: -0.75 + x = 1.457737974 Solving -0.75 + x = 1.457737974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.457737974 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.457737974 + 0.75 x = 1.457737974 + 0.75 Combine like terms: 1.457737974 + 0.75 = 2.207737974 x = 2.207737974 Simplifying x = 2.207737974

Subproblem 2

x + -0.75 = -1.457737974 Simplifying x + -0.75 = -1.457737974 Reorder the terms: -0.75 + x = -1.457737974 Solving -0.75 + x = -1.457737974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.457737974 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.457737974 + 0.75 x = -1.457737974 + 0.75 Combine like terms: -1.457737974 + 0.75 = -0.707737974 x = -0.707737974 Simplifying x = -0.707737974

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.207737974, -0.707737974}

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