4x*x+10x-11=0

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Solution for 4x*x+10x-11=0 equation:


Simplifying
4x * x + 10x + -11 = 0

Multiply x * x
4x2 + 10x + -11 = 0

Reorder the terms:
-11 + 10x + 4x2 = 0

Solving
-11 + 10x + 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'.
-2.75 + 2.5x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 2.5x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 2.5x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 2.5x + x2 = 0 + 2.75
2.5x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
2.5x + x2 = 2.75

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 2.75 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 2.75 + 1.5625

Combine like terms: 2.75 + 1.5625 = 4.3125
1.5625 + 2.5x + x2 = 4.3125

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 4.3125

Calculate the square root of the right side: 2.076655966

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.076655966 and -2.076655966.

Subproblem 1

x + 1.25 = 2.076655966 Simplifying x + 1.25 = 2.076655966 Reorder the terms: 1.25 + x = 2.076655966 Solving 1.25 + x = 2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.076655966 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.076655966 + -1.25 x = 2.076655966 + -1.25 Combine like terms: 2.076655966 + -1.25 = 0.826655966 x = 0.826655966 Simplifying x = 0.826655966

Subproblem 2

x + 1.25 = -2.076655966 Simplifying x + 1.25 = -2.076655966 Reorder the terms: 1.25 + x = -2.076655966 Solving 1.25 + x = -2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.076655966 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.076655966 + -1.25 x = -2.076655966 + -1.25 Combine like terms: -2.076655966 + -1.25 = -3.326655966 x = -3.326655966 Simplifying x = -3.326655966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.826655966, -3.326655966}

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