4x^2-15x+11=2x+2

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Solution for 4x^2-15x+11=2x+2 equation:


Simplifying
4x2 + -15x + 11 = 2x + 2

Reorder the terms:
11 + -15x + 4x2 = 2x + 2

Reorder the terms:
11 + -15x + 4x2 = 2 + 2x

Solving
11 + -15x + 4x2 = 2 + 2x

Solving for variable 'x'.

Reorder the terms:
11 + -2 + -15x + -2x + 4x2 = 2 + 2x + -2 + -2x

Combine like terms: 11 + -2 = 9
9 + -15x + -2x + 4x2 = 2 + 2x + -2 + -2x

Combine like terms: -15x + -2x = -17x
9 + -17x + 4x2 = 2 + 2x + -2 + -2x

Reorder the terms:
9 + -17x + 4x2 = 2 + -2 + 2x + -2x

Combine like terms: 2 + -2 = 0
9 + -17x + 4x2 = 0 + 2x + -2x
9 + -17x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
9 + -17x + 4x2 = 0

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

Divide each side by '4'.
2.25 + -4.25x + x2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -4.25x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -4.25x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -4.25x + x2 = 0 + -2.25
-4.25x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-4.25x + x2 = -2.25

The x term is -4.25x.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25x + 4.515625 + x2 = -2.25 + 4.515625

Reorder the terms:
4.515625 + -4.25x + x2 = -2.25 + 4.515625

Combine like terms: -2.25 + 4.515625 = 2.265625
4.515625 + -4.25x + x2 = 2.265625

Factor a perfect square on the left side:
(x + -2.125)(x + -2.125) = 2.265625

Calculate the square root of the right side: 1.505199322

Break this problem into two subproblems by setting 
(x + -2.125) equal to 1.505199322 and -1.505199322.

Subproblem 1

x + -2.125 = 1.505199322 Simplifying x + -2.125 = 1.505199322 Reorder the terms: -2.125 + x = 1.505199322 Solving -2.125 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 1.505199322 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 1.505199322 + 2.125 x = 1.505199322 + 2.125 Combine like terms: 1.505199322 + 2.125 = 3.630199322 x = 3.630199322 Simplifying x = 3.630199322

Subproblem 2

x + -2.125 = -1.505199322 Simplifying x + -2.125 = -1.505199322 Reorder the terms: -2.125 + x = -1.505199322 Solving -2.125 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -1.505199322 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -1.505199322 + 2.125 x = -1.505199322 + 2.125 Combine like terms: -1.505199322 + 2.125 = 0.619800678 x = 0.619800678 Simplifying x = 0.619800678

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.630199322, 0.619800678}

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