16x^2-9x-63=0

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Solution for 16x^2-9x-63=0 equation:


Simplifying
16x2 + -9x + -63 = 0

Reorder the terms:
-63 + -9x + 16x2 = 0

Solving
-63 + -9x + 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'.
-3.9375 + -0.5625x + x2 = 0

Move the constant term to the right:

Add '3.9375' to each side of the equation.
-3.9375 + -0.5625x + 3.9375 + x2 = 0 + 3.9375

Reorder the terms:
-3.9375 + 3.9375 + -0.5625x + x2 = 0 + 3.9375

Combine like terms: -3.9375 + 3.9375 = 0.0000
0.0000 + -0.5625x + x2 = 0 + 3.9375
-0.5625x + x2 = 0 + 3.9375

Combine like terms: 0 + 3.9375 = 3.9375
-0.5625x + x2 = 3.9375

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 = 3.9375 + 0.0791015625

Reorder the terms:
0.0791015625 + -0.5625x + x2 = 3.9375 + 0.0791015625

Combine like terms: 3.9375 + 0.0791015625 = 4.0166015625
0.0791015625 + -0.5625x + x2 = 4.0166015625

Factor a perfect square on the left side:
(x + -0.28125)(x + -0.28125) = 4.0166015625

Calculate the square root of the right side: 2.004146093

Break this problem into two subproblems by setting 
(x + -0.28125) equal to 2.004146093 and -2.004146093.

Subproblem 1

x + -0.28125 = 2.004146093 Simplifying x + -0.28125 = 2.004146093 Reorder the terms: -0.28125 + x = 2.004146093 Solving -0.28125 + x = 2.004146093 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 = 2.004146093 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = 2.004146093 + 0.28125 x = 2.004146093 + 0.28125 Combine like terms: 2.004146093 + 0.28125 = 2.285396093 x = 2.285396093 Simplifying x = 2.285396093

Subproblem 2

x + -0.28125 = -2.004146093 Simplifying x + -0.28125 = -2.004146093 Reorder the terms: -0.28125 + x = -2.004146093 Solving -0.28125 + x = -2.004146093 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 = -2.004146093 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = -2.004146093 + 0.28125 x = -2.004146093 + 0.28125 Combine like terms: -2.004146093 + 0.28125 = -1.722896093 x = -1.722896093 Simplifying x = -1.722896093

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.285396093, -1.722896093}

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