28x^2+11x-25=0

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Solution for 28x^2+11x-25=0 equation:


Simplifying
28x2 + 11x + -25 = 0

Reorder the terms:
-25 + 11x + 28x2 = 0

Solving
-25 + 11x + 28x2 = 0

Solving for variable 'x'.

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

Divide each side by '28'.
-0.8928571429 + 0.3928571429x + x2 = 0

Move the constant term to the right:

Add '0.8928571429' to each side of the equation.
-0.8928571429 + 0.3928571429x + 0.8928571429 + x2 = 0 + 0.8928571429

Reorder the terms:
-0.8928571429 + 0.8928571429 + 0.3928571429x + x2 = 0 + 0.8928571429

Combine like terms: -0.8928571429 + 0.8928571429 = 0.0000000000
0.0000000000 + 0.3928571429x + x2 = 0 + 0.8928571429
0.3928571429x + x2 = 0 + 0.8928571429

Combine like terms: 0 + 0.8928571429 = 0.8928571429
0.3928571429x + x2 = 0.8928571429

The x term is 0.3928571429x.  Take half its coefficient (0.1964285715).
Square it (0.03858418370) and add it to both sides.

Add '0.03858418370' to each side of the equation.
0.3928571429x + 0.03858418370 + x2 = 0.8928571429 + 0.03858418370

Reorder the terms:
0.03858418370 + 0.3928571429x + x2 = 0.8928571429 + 0.03858418370

Combine like terms: 0.8928571429 + 0.03858418370 = 0.9314413266
0.03858418370 + 0.3928571429x + x2 = 0.9314413266

Factor a perfect square on the left side:
(x + 0.1964285715)(x + 0.1964285715) = 0.9314413266

Calculate the square root of the right side: 0.96511208

Break this problem into two subproblems by setting 
(x + 0.1964285715) equal to 0.96511208 and -0.96511208.

Subproblem 1

x + 0.1964285715 = 0.96511208 Simplifying x + 0.1964285715 = 0.96511208 Reorder the terms: 0.1964285715 + x = 0.96511208 Solving 0.1964285715 + x = 0.96511208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1964285715' to each side of the equation. 0.1964285715 + -0.1964285715 + x = 0.96511208 + -0.1964285715 Combine like terms: 0.1964285715 + -0.1964285715 = 0.0000000000 0.0000000000 + x = 0.96511208 + -0.1964285715 x = 0.96511208 + -0.1964285715 Combine like terms: 0.96511208 + -0.1964285715 = 0.7686835085 x = 0.7686835085 Simplifying x = 0.7686835085

Subproblem 2

x + 0.1964285715 = -0.96511208 Simplifying x + 0.1964285715 = -0.96511208 Reorder the terms: 0.1964285715 + x = -0.96511208 Solving 0.1964285715 + x = -0.96511208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1964285715' to each side of the equation. 0.1964285715 + -0.1964285715 + x = -0.96511208 + -0.1964285715 Combine like terms: 0.1964285715 + -0.1964285715 = 0.0000000000 0.0000000000 + x = -0.96511208 + -0.1964285715 x = -0.96511208 + -0.1964285715 Combine like terms: -0.96511208 + -0.1964285715 = -1.1615406515 x = -1.1615406515 Simplifying x = -1.1615406515

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7686835085, -1.1615406515}

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