16x^2-40x+7=0

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Solution for 16x^2-40x+7=0 equation:


Simplifying
16x2 + -40x + 7 = 0

Reorder the terms:
7 + -40x + 16x2 = 0

Solving
7 + -40x + 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'.
0.4375 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-0.4375' to each side of the equation.
0.4375 + -2.5x + -0.4375 + x2 = 0 + -0.4375

Reorder the terms:
0.4375 + -0.4375 + -2.5x + x2 = 0 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + -2.5x + x2 = 0 + -0.4375
-2.5x + x2 = 0 + -0.4375

Combine like terms: 0 + -0.4375 = -0.4375
-2.5x + x2 = -0.4375

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -0.4375 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -0.4375 + 1.5625

Combine like terms: -0.4375 + 1.5625 = 1.125
1.5625 + -2.5x + x2 = 1.125

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 1.125

Calculate the square root of the right side: 1.060660172

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.060660172 and -1.060660172.

Subproblem 1

x + -1.25 = 1.060660172 Simplifying x + -1.25 = 1.060660172 Reorder the terms: -1.25 + x = 1.060660172 Solving -1.25 + x = 1.060660172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.060660172 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.060660172 + 1.25 x = 1.060660172 + 1.25 Combine like terms: 1.060660172 + 1.25 = 2.310660172 x = 2.310660172 Simplifying x = 2.310660172

Subproblem 2

x + -1.25 = -1.060660172 Simplifying x + -1.25 = -1.060660172 Reorder the terms: -1.25 + x = -1.060660172 Solving -1.25 + x = -1.060660172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.060660172 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.060660172 + 1.25 x = -1.060660172 + 1.25 Combine like terms: -1.060660172 + 1.25 = 0.189339828 x = 0.189339828 Simplifying x = 0.189339828

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.310660172, 0.189339828}

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