16x^2+150x-15=0

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Solution for 16x^2+150x-15=0 equation:


Simplifying
16x2 + 150x + -15 = 0

Reorder the terms:
-15 + 150x + 16x2 = 0

Solving
-15 + 150x + 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'.
-0.9375 + 9.375x + x2 = 0

Move the constant term to the right:

Add '0.9375' to each side of the equation.
-0.9375 + 9.375x + 0.9375 + x2 = 0 + 0.9375

Reorder the terms:
-0.9375 + 0.9375 + 9.375x + x2 = 0 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + 9.375x + x2 = 0 + 0.9375
9.375x + x2 = 0 + 0.9375

Combine like terms: 0 + 0.9375 = 0.9375
9.375x + x2 = 0.9375

The x term is 9.375x.  Take half its coefficient (4.6875).
Square it (21.97265625) and add it to both sides.

Add '21.97265625' to each side of the equation.
9.375x + 21.97265625 + x2 = 0.9375 + 21.97265625

Reorder the terms:
21.97265625 + 9.375x + x2 = 0.9375 + 21.97265625

Combine like terms: 0.9375 + 21.97265625 = 22.91015625
21.97265625 + 9.375x + x2 = 22.91015625

Factor a perfect square on the left side:
(x + 4.6875)(x + 4.6875) = 22.91015625

Calculate the square root of the right side: 4.7864555

Break this problem into two subproblems by setting 
(x + 4.6875) equal to 4.7864555 and -4.7864555.

Subproblem 1

x + 4.6875 = 4.7864555 Simplifying x + 4.6875 = 4.7864555 Reorder the terms: 4.6875 + x = 4.7864555 Solving 4.6875 + x = 4.7864555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + x = 4.7864555 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = 4.7864555 + -4.6875 x = 4.7864555 + -4.6875 Combine like terms: 4.7864555 + -4.6875 = 0.0989555 x = 0.0989555 Simplifying x = 0.0989555

Subproblem 2

x + 4.6875 = -4.7864555 Simplifying x + 4.6875 = -4.7864555 Reorder the terms: 4.6875 + x = -4.7864555 Solving 4.6875 + x = -4.7864555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + x = -4.7864555 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = -4.7864555 + -4.6875 x = -4.7864555 + -4.6875 Combine like terms: -4.7864555 + -4.6875 = -9.4739555 x = -9.4739555 Simplifying x = -9.4739555

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.0989555, -9.4739555}

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