7x^2-19x-48=0

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Solution for 7x^2-19x-48=0 equation:


Simplifying
7x2 + -19x + -48 = 0

Reorder the terms:
-48 + -19x + 7x2 = 0

Solving
-48 + -19x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-6.857142857 + -2.714285714x + x2 = 0

Move the constant term to the right:

Add '6.857142857' to each side of the equation.
-6.857142857 + -2.714285714x + 6.857142857 + x2 = 0 + 6.857142857

Reorder the terms:
-6.857142857 + 6.857142857 + -2.714285714x + x2 = 0 + 6.857142857

Combine like terms: -6.857142857 + 6.857142857 = 0.000000000
0.000000000 + -2.714285714x + x2 = 0 + 6.857142857
-2.714285714x + x2 = 0 + 6.857142857

Combine like terms: 0 + 6.857142857 = 6.857142857
-2.714285714x + x2 = 6.857142857

The x term is -2.714285714x.  Take half its coefficient (-1.357142857).
Square it (1.841836734) and add it to both sides.

Add '1.841836734' to each side of the equation.
-2.714285714x + 1.841836734 + x2 = 6.857142857 + 1.841836734

Reorder the terms:
1.841836734 + -2.714285714x + x2 = 6.857142857 + 1.841836734

Combine like terms: 6.857142857 + 1.841836734 = 8.698979591
1.841836734 + -2.714285714x + x2 = 8.698979591

Factor a perfect square on the left side:
(x + -1.357142857)(x + -1.357142857) = 8.698979591

Calculate the square root of the right side: 2.94940326

Break this problem into two subproblems by setting 
(x + -1.357142857) equal to 2.94940326 and -2.94940326.

Subproblem 1

x + -1.357142857 = 2.94940326 Simplifying x + -1.357142857 = 2.94940326 Reorder the terms: -1.357142857 + x = 2.94940326 Solving -1.357142857 + x = 2.94940326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + x = 2.94940326 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = 2.94940326 + 1.357142857 x = 2.94940326 + 1.357142857 Combine like terms: 2.94940326 + 1.357142857 = 4.306546117 x = 4.306546117 Simplifying x = 4.306546117

Subproblem 2

x + -1.357142857 = -2.94940326 Simplifying x + -1.357142857 = -2.94940326 Reorder the terms: -1.357142857 + x = -2.94940326 Solving -1.357142857 + x = -2.94940326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + x = -2.94940326 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = -2.94940326 + 1.357142857 x = -2.94940326 + 1.357142857 Combine like terms: -2.94940326 + 1.357142857 = -1.592260403 x = -1.592260403 Simplifying x = -1.592260403

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.306546117, -1.592260403}

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