4x^2-29x+15=-9+6

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Solution for 4x^2-29x+15=-9+6 equation:


Simplifying
4x2 + -29x + 15 = -9 + 6

Reorder the terms:
15 + -29x + 4x2 = -9 + 6

Combine like terms: -9 + 6 = -3
15 + -29x + 4x2 = -3

Solving
15 + -29x + 4x2 = -3

Solving for variable 'x'.

Reorder the terms:
15 + 3 + -29x + 4x2 = -3 + 3

Combine like terms: 15 + 3 = 18
18 + -29x + 4x2 = -3 + 3

Combine like terms: -3 + 3 = 0
18 + -29x + 4x2 = 0

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

Divide each side by '4'.
4.5 + -7.25x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -7.25x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -7.25x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -7.25x + x2 = 0 + -4.5
-7.25x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-7.25x + x2 = -4.5

The x term is -7.25x.  Take half its coefficient (-3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
-7.25x + 13.140625 + x2 = -4.5 + 13.140625

Reorder the terms:
13.140625 + -7.25x + x2 = -4.5 + 13.140625

Combine like terms: -4.5 + 13.140625 = 8.640625
13.140625 + -7.25x + x2 = 8.640625

Factor a perfect square on the left side:
(x + -3.625)(x + -3.625) = 8.640625

Calculate the square root of the right side: 2.939494004

Break this problem into two subproblems by setting 
(x + -3.625) equal to 2.939494004 and -2.939494004.

Subproblem 1

x + -3.625 = 2.939494004 Simplifying x + -3.625 = 2.939494004 Reorder the terms: -3.625 + x = 2.939494004 Solving -3.625 + x = 2.939494004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 2.939494004 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 2.939494004 + 3.625 x = 2.939494004 + 3.625 Combine like terms: 2.939494004 + 3.625 = 6.564494004 x = 6.564494004 Simplifying x = 6.564494004

Subproblem 2

x + -3.625 = -2.939494004 Simplifying x + -3.625 = -2.939494004 Reorder the terms: -3.625 + x = -2.939494004 Solving -3.625 + x = -2.939494004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -2.939494004 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -2.939494004 + 3.625 x = -2.939494004 + 3.625 Combine like terms: -2.939494004 + 3.625 = 0.685505996 x = 0.685505996 Simplifying x = 0.685505996

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.564494004, 0.685505996}

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