95=16x^2+9x

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Solution for 95=16x^2+9x equation:


Simplifying
95 = 16x2 + 9x

Reorder the terms:
95 = 9x + 16x2

Solving
95 = 9x + 16x2

Solving for variable 'x'.

Reorder the terms:
95 + -9x + -16x2 = 9x + -9x + 16x2 + -16x2

Combine like terms: 9x + -9x = 0
95 + -9x + -16x2 = 0 + 16x2 + -16x2
95 + -9x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
95 + -9x + -16x2 = 0

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

Divide each side by '-16'.
-5.9375 + 0.5625x + x2 = 0

Move the constant term to the right:

Add '5.9375' to each side of the equation.
-5.9375 + 0.5625x + 5.9375 + x2 = 0 + 5.9375

Reorder the terms:
-5.9375 + 5.9375 + 0.5625x + x2 = 0 + 5.9375

Combine like terms: -5.9375 + 5.9375 = 0.0000
0.0000 + 0.5625x + x2 = 0 + 5.9375
0.5625x + x2 = 0 + 5.9375

Combine like terms: 0 + 5.9375 = 5.9375
0.5625x + x2 = 5.9375

The x term is 0.5625x.  Take half its coefficient (0.28125).
Square it (0.0791015625) and add it to both sides.

Add '0.0791015625' to each side of the equation.
0.5625x + 0.0791015625 + x2 = 5.9375 + 0.0791015625

Reorder the terms:
0.0791015625 + 0.5625x + x2 = 5.9375 + 0.0791015625

Combine like terms: 5.9375 + 0.0791015625 = 6.0166015625
0.0791015625 + 0.5625x + x2 = 6.0166015625

Factor a perfect square on the left side:
(x + 0.28125)(x + 0.28125) = 6.0166015625

Calculate the square root of the right side: 2.452876182

Break this problem into two subproblems by setting 
(x + 0.28125) equal to 2.452876182 and -2.452876182.

Subproblem 1

x + 0.28125 = 2.452876182 Simplifying x + 0.28125 = 2.452876182 Reorder the terms: 0.28125 + x = 2.452876182 Solving 0.28125 + x = 2.452876182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = 2.452876182 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = 2.452876182 + -0.28125 x = 2.452876182 + -0.28125 Combine like terms: 2.452876182 + -0.28125 = 2.171626182 x = 2.171626182 Simplifying x = 2.171626182

Subproblem 2

x + 0.28125 = -2.452876182 Simplifying x + 0.28125 = -2.452876182 Reorder the terms: 0.28125 + x = -2.452876182 Solving 0.28125 + x = -2.452876182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = -2.452876182 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = -2.452876182 + -0.28125 x = -2.452876182 + -0.28125 Combine like terms: -2.452876182 + -0.28125 = -2.734126182 x = -2.734126182 Simplifying x = -2.734126182

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.171626182, -2.734126182}

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