4x^2-11x-7=0

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Solution for 4x^2-11x-7=0 equation:


Simplifying
4x2 + -11x + -7 = 0

Reorder the terms:
-7 + -11x + 4x2 = 0

Solving
-7 + -11x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-1.75 + -2.75x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -2.75x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -2.75x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -2.75x + x2 = 0 + 1.75
-2.75x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-2.75x + x2 = 1.75

The x term is -2.75x.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75x + 1.890625 + x2 = 1.75 + 1.890625

Reorder the terms:
1.890625 + -2.75x + x2 = 1.75 + 1.890625

Combine like terms: 1.75 + 1.890625 = 3.640625
1.890625 + -2.75x + x2 = 3.640625

Factor a perfect square on the left side:
(x + -1.375)(x + -1.375) = 3.640625

Calculate the square root of the right side: 1.90804219

Break this problem into two subproblems by setting 
(x + -1.375) equal to 1.90804219 and -1.90804219.

Subproblem 1

x + -1.375 = 1.90804219 Simplifying x + -1.375 = 1.90804219 Reorder the terms: -1.375 + x = 1.90804219 Solving -1.375 + x = 1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 1.90804219 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.90804219 + 1.375 x = 1.90804219 + 1.375 Combine like terms: 1.90804219 + 1.375 = 3.28304219 x = 3.28304219 Simplifying x = 3.28304219

Subproblem 2

x + -1.375 = -1.90804219 Simplifying x + -1.375 = -1.90804219 Reorder the terms: -1.375 + x = -1.90804219 Solving -1.375 + x = -1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -1.90804219 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.90804219 + 1.375 x = -1.90804219 + 1.375 Combine like terms: -1.90804219 + 1.375 = -0.53304219 x = -0.53304219 Simplifying x = -0.53304219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.28304219, -0.53304219}

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