16x^2+7x-2=

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


Simplifying
16x2 + 7x + -2 = 0

Reorder the terms:
-2 + 7x + 16x2 = 0

Solving
-2 + 7x + 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'.
-0.125 + 0.4375x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 0.4375x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 0.4375x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 0.4375x + x2 = 0 + 0.125
0.4375x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
0.4375x + x2 = 0.125

The x term is 0.4375x.  Take half its coefficient (0.21875).
Square it (0.0478515625) and add it to both sides.

Add '0.0478515625' to each side of the equation.
0.4375x + 0.0478515625 + x2 = 0.125 + 0.0478515625

Reorder the terms:
0.0478515625 + 0.4375x + x2 = 0.125 + 0.0478515625

Combine like terms: 0.125 + 0.0478515625 = 0.1728515625
0.0478515625 + 0.4375x + x2 = 0.1728515625

Factor a perfect square on the left side:
(x + 0.21875)(x + 0.21875) = 0.1728515625

Calculate the square root of the right side: 0.415754209

Break this problem into two subproblems by setting 
(x + 0.21875) equal to 0.415754209 and -0.415754209.

Subproblem 1

x + 0.21875 = 0.415754209 Simplifying x + 0.21875 = 0.415754209 Reorder the terms: 0.21875 + x = 0.415754209 Solving 0.21875 + x = 0.415754209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + x = 0.415754209 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + x = 0.415754209 + -0.21875 x = 0.415754209 + -0.21875 Combine like terms: 0.415754209 + -0.21875 = 0.197004209 x = 0.197004209 Simplifying x = 0.197004209

Subproblem 2

x + 0.21875 = -0.415754209 Simplifying x + 0.21875 = -0.415754209 Reorder the terms: 0.21875 + x = -0.415754209 Solving 0.21875 + x = -0.415754209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + x = -0.415754209 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + x = -0.415754209 + -0.21875 x = -0.415754209 + -0.21875 Combine like terms: -0.415754209 + -0.21875 = -0.634504209 x = -0.634504209 Simplifying x = -0.634504209

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.197004209, -0.634504209}

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