-16x^2+28x+25=0

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Solution for -16x^2+28x+25=0 equation:


Simplifying
-16x2 + 28x + 25 = 0

Reorder the terms:
25 + 28x + -16x2 = 0

Solving
25 + 28x + -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 + -1.75x + x2 = 0

Move the constant term to the right:

Add '1.5625' to each side of the equation.
-1.5625 + -1.75x + 1.5625 + x2 = 0 + 1.5625

Reorder the terms:
-1.5625 + 1.5625 + -1.75x + x2 = 0 + 1.5625

Combine like terms: -1.5625 + 1.5625 = 0.0000
0.0000 + -1.75x + x2 = 0 + 1.5625
-1.75x + x2 = 0 + 1.5625

Combine like terms: 0 + 1.5625 = 1.5625
-1.75x + x2 = 1.5625

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 1.5625 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 1.5625 + 0.765625

Combine like terms: 1.5625 + 0.765625 = 2.328125
0.765625 + -1.75x + x2 = 2.328125

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 2.328125

Calculate the square root of the right side: 1.525819452

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.525819452 and -1.525819452.

Subproblem 1

x + -0.875 = 1.525819452 Simplifying x + -0.875 = 1.525819452 Reorder the terms: -0.875 + x = 1.525819452 Solving -0.875 + x = 1.525819452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 1.525819452 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.525819452 + 0.875 x = 1.525819452 + 0.875 Combine like terms: 1.525819452 + 0.875 = 2.400819452 x = 2.400819452 Simplifying x = 2.400819452

Subproblem 2

x + -0.875 = -1.525819452 Simplifying x + -0.875 = -1.525819452 Reorder the terms: -0.875 + x = -1.525819452 Solving -0.875 + x = -1.525819452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -1.525819452 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.525819452 + 0.875 x = -1.525819452 + 0.875 Combine like terms: -1.525819452 + 0.875 = -0.650819452 x = -0.650819452 Simplifying x = -0.650819452

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.400819452, -0.650819452}

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