45x^2+49x-8=0

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Solution for 45x^2+49x-8=0 equation:


Simplifying
45x2 + 49x + -8 = 0

Reorder the terms:
-8 + 49x + 45x2 = 0

Solving
-8 + 49x + 45x2 = 0

Solving for variable 'x'.

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

Divide each side by '45'.
-0.1777777778 + 1.088888889x + x2 = 0

Move the constant term to the right:

Add '0.1777777778' to each side of the equation.
-0.1777777778 + 1.088888889x + 0.1777777778 + x2 = 0 + 0.1777777778

Reorder the terms:
-0.1777777778 + 0.1777777778 + 1.088888889x + x2 = 0 + 0.1777777778

Combine like terms: -0.1777777778 + 0.1777777778 = 0.0000000000
0.0000000000 + 1.088888889x + x2 = 0 + 0.1777777778
1.088888889x + x2 = 0 + 0.1777777778

Combine like terms: 0 + 0.1777777778 = 0.1777777778
1.088888889x + x2 = 0.1777777778

The x term is 1.088888889x.  Take half its coefficient (0.5444444445).
Square it (0.2964197531) and add it to both sides.

Add '0.2964197531' to each side of the equation.
1.088888889x + 0.2964197531 + x2 = 0.1777777778 + 0.2964197531

Reorder the terms:
0.2964197531 + 1.088888889x + x2 = 0.1777777778 + 0.2964197531

Combine like terms: 0.1777777778 + 0.2964197531 = 0.4741975309
0.2964197531 + 1.088888889x + x2 = 0.4741975309

Factor a perfect square on the left side:
(x + 0.5444444445)(x + 0.5444444445) = 0.4741975309

Calculate the square root of the right side: 0.688620019

Break this problem into two subproblems by setting 
(x + 0.5444444445) equal to 0.688620019 and -0.688620019.

Subproblem 1

x + 0.5444444445 = 0.688620019 Simplifying x + 0.5444444445 = 0.688620019 Reorder the terms: 0.5444444445 + x = 0.688620019 Solving 0.5444444445 + x = 0.688620019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5444444445' to each side of the equation. 0.5444444445 + -0.5444444445 + x = 0.688620019 + -0.5444444445 Combine like terms: 0.5444444445 + -0.5444444445 = 0.0000000000 0.0000000000 + x = 0.688620019 + -0.5444444445 x = 0.688620019 + -0.5444444445 Combine like terms: 0.688620019 + -0.5444444445 = 0.1441755745 x = 0.1441755745 Simplifying x = 0.1441755745

Subproblem 2

x + 0.5444444445 = -0.688620019 Simplifying x + 0.5444444445 = -0.688620019 Reorder the terms: 0.5444444445 + x = -0.688620019 Solving 0.5444444445 + x = -0.688620019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5444444445' to each side of the equation. 0.5444444445 + -0.5444444445 + x = -0.688620019 + -0.5444444445 Combine like terms: 0.5444444445 + -0.5444444445 = 0.0000000000 0.0000000000 + x = -0.688620019 + -0.5444444445 x = -0.688620019 + -0.5444444445 Combine like terms: -0.688620019 + -0.5444444445 = -1.2330644635 x = -1.2330644635 Simplifying x = -1.2330644635

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1441755745, -1.2330644635}

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