5x^2-22x+15=0

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Solution for 5x^2-22x+15=0 equation:


Simplifying
5x2 + -22x + 15 = 0

Reorder the terms:
15 + -22x + 5x2 = 0

Solving
15 + -22x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
3 + -4.4x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -4.4x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -4.4x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4.4x + x2 = 0 + -3
-4.4x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-4.4x + x2 = -3

The x term is -4.4x.  Take half its coefficient (-2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
-4.4x + 4.84 + x2 = -3 + 4.84

Reorder the terms:
4.84 + -4.4x + x2 = -3 + 4.84

Combine like terms: -3 + 4.84 = 1.84
4.84 + -4.4x + x2 = 1.84

Factor a perfect square on the left side:
(x + -2.2)(x + -2.2) = 1.84

Calculate the square root of the right side: 1.356465997

Break this problem into two subproblems by setting 
(x + -2.2) equal to 1.356465997 and -1.356465997.

Subproblem 1

x + -2.2 = 1.356465997 Simplifying x + -2.2 = 1.356465997 Reorder the terms: -2.2 + x = 1.356465997 Solving -2.2 + x = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 1.356465997 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 1.356465997 + 2.2 x = 1.356465997 + 2.2 Combine like terms: 1.356465997 + 2.2 = 3.556465997 x = 3.556465997 Simplifying x = 3.556465997

Subproblem 2

x + -2.2 = -1.356465997 Simplifying x + -2.2 = -1.356465997 Reorder the terms: -2.2 + x = -1.356465997 Solving -2.2 + x = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -1.356465997 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -1.356465997 + 2.2 x = -1.356465997 + 2.2 Combine like terms: -1.356465997 + 2.2 = 0.843534003 x = 0.843534003 Simplifying x = 0.843534003

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.556465997, 0.843534003}

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