-15+22x+28x^2=0

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Solution for -15+22x+28x^2=0 equation:


Simplifying
-15 + 22x + 28x2 = 0

Solving
-15 + 22x + 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'.
-0.5357142857 + 0.7857142857x + x2 = 0

Move the constant term to the right:

Add '0.5357142857' to each side of the equation.
-0.5357142857 + 0.7857142857x + 0.5357142857 + x2 = 0 + 0.5357142857

Reorder the terms:
-0.5357142857 + 0.5357142857 + 0.7857142857x + x2 = 0 + 0.5357142857

Combine like terms: -0.5357142857 + 0.5357142857 = 0.0000000000
0.0000000000 + 0.7857142857x + x2 = 0 + 0.5357142857
0.7857142857x + x2 = 0 + 0.5357142857

Combine like terms: 0 + 0.5357142857 = 0.5357142857
0.7857142857x + x2 = 0.5357142857

The x term is 0.7857142857x.  Take half its coefficient (0.3928571429).
Square it (0.1543367347) and add it to both sides.

Add '0.1543367347' to each side of the equation.
0.7857142857x + 0.1543367347 + x2 = 0.5357142857 + 0.1543367347

Reorder the terms:
0.1543367347 + 0.7857142857x + x2 = 0.5357142857 + 0.1543367347

Combine like terms: 0.5357142857 + 0.1543367347 = 0.6900510204
0.1543367347 + 0.7857142857x + x2 = 0.6900510204

Factor a perfect square on the left side:
(x + 0.3928571429)(x + 0.3928571429) = 0.6900510204

Calculate the square root of the right side: 0.830693096

Break this problem into two subproblems by setting 
(x + 0.3928571429) equal to 0.830693096 and -0.830693096.

Subproblem 1

x + 0.3928571429 = 0.830693096 Simplifying x + 0.3928571429 = 0.830693096 Reorder the terms: 0.3928571429 + x = 0.830693096 Solving 0.3928571429 + x = 0.830693096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3928571429' to each side of the equation. 0.3928571429 + -0.3928571429 + x = 0.830693096 + -0.3928571429 Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000 0.0000000000 + x = 0.830693096 + -0.3928571429 x = 0.830693096 + -0.3928571429 Combine like terms: 0.830693096 + -0.3928571429 = 0.4378359531 x = 0.4378359531 Simplifying x = 0.4378359531

Subproblem 2

x + 0.3928571429 = -0.830693096 Simplifying x + 0.3928571429 = -0.830693096 Reorder the terms: 0.3928571429 + x = -0.830693096 Solving 0.3928571429 + x = -0.830693096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3928571429' to each side of the equation. 0.3928571429 + -0.3928571429 + x = -0.830693096 + -0.3928571429 Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000 0.0000000000 + x = -0.830693096 + -0.3928571429 x = -0.830693096 + -0.3928571429 Combine like terms: -0.830693096 + -0.3928571429 = -1.2235502389 x = -1.2235502389 Simplifying x = -1.2235502389

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4378359531, -1.2235502389}

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