x^2-17x^2+39x+297=0

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Solution for x^2-17x^2+39x+297=0 equation:


Simplifying
x2 + -17x2 + 39x + 297 = 0

Reorder the terms:
297 + 39x + x2 + -17x2 = 0

Combine like terms: x2 + -17x2 = -16x2
297 + 39x + -16x2 = 0

Solving
297 + 39x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-18.5625 + -2.4375x + x2 = 0

Move the constant term to the right:

Add '18.5625' to each side of the equation.
-18.5625 + -2.4375x + 18.5625 + x2 = 0 + 18.5625

Reorder the terms:
-18.5625 + 18.5625 + -2.4375x + x2 = 0 + 18.5625

Combine like terms: -18.5625 + 18.5625 = 0.0000
0.0000 + -2.4375x + x2 = 0 + 18.5625
-2.4375x + x2 = 0 + 18.5625

Combine like terms: 0 + 18.5625 = 18.5625
-2.4375x + x2 = 18.5625

The x term is -2.4375x.  Take half its coefficient (-1.21875).
Square it (1.485351563) and add it to both sides.

Add '1.485351563' to each side of the equation.
-2.4375x + 1.485351563 + x2 = 18.5625 + 1.485351563

Reorder the terms:
1.485351563 + -2.4375x + x2 = 18.5625 + 1.485351563

Combine like terms: 18.5625 + 1.485351563 = 20.047851563
1.485351563 + -2.4375x + x2 = 20.047851563

Factor a perfect square on the left side:
(x + -1.21875)(x + -1.21875) = 20.047851563

Calculate the square root of the right side: 4.477482726

Break this problem into two subproblems by setting 
(x + -1.21875) equal to 4.477482726 and -4.477482726.

Subproblem 1

x + -1.21875 = 4.477482726 Simplifying x + -1.21875 = 4.477482726 Reorder the terms: -1.21875 + x = 4.477482726 Solving -1.21875 + x = 4.477482726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.21875' to each side of the equation. -1.21875 + 1.21875 + x = 4.477482726 + 1.21875 Combine like terms: -1.21875 + 1.21875 = 0.00000 0.00000 + x = 4.477482726 + 1.21875 x = 4.477482726 + 1.21875 Combine like terms: 4.477482726 + 1.21875 = 5.696232726 x = 5.696232726 Simplifying x = 5.696232726

Subproblem 2

x + -1.21875 = -4.477482726 Simplifying x + -1.21875 = -4.477482726 Reorder the terms: -1.21875 + x = -4.477482726 Solving -1.21875 + x = -4.477482726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.21875' to each side of the equation. -1.21875 + 1.21875 + x = -4.477482726 + 1.21875 Combine like terms: -1.21875 + 1.21875 = 0.00000 0.00000 + x = -4.477482726 + 1.21875 x = -4.477482726 + 1.21875 Combine like terms: -4.477482726 + 1.21875 = -3.258732726 x = -3.258732726 Simplifying x = -3.258732726

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.696232726, -3.258732726}

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