4.905x^2-16x-7=0

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Solution for 4.905x^2-16x-7=0 equation:


Simplifying
4.905x2 + -16x + -7 = 0

Reorder the terms:
-7 + -16x + 4.905x2 = 0

Solving
-7 + -16x + 4.905x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.905'.
-1.427115189 + -3.261977574x + x2 = 0

Move the constant term to the right:

Add '1.427115189' to each side of the equation.
-1.427115189 + -3.261977574x + 1.427115189 + x2 = 0 + 1.427115189

Reorder the terms:
-1.427115189 + 1.427115189 + -3.261977574x + x2 = 0 + 1.427115189

Combine like terms: -1.427115189 + 1.427115189 = 0.000000000
0.000000000 + -3.261977574x + x2 = 0 + 1.427115189
-3.261977574x + x2 = 0 + 1.427115189

Combine like terms: 0 + 1.427115189 = 1.427115189
-3.261977574x + x2 = 1.427115189

The x term is -3.261977574x.  Take half its coefficient (-1.630988787).
Square it (2.660124423) and add it to both sides.

Add '2.660124423' to each side of the equation.
-3.261977574x + 2.660124423 + x2 = 1.427115189 + 2.660124423

Reorder the terms:
2.660124423 + -3.261977574x + x2 = 1.427115189 + 2.660124423

Combine like terms: 1.427115189 + 2.660124423 = 4.087239612
2.660124423 + -3.261977574x + x2 = 4.087239612

Factor a perfect square on the left side:
(x + -1.630988787)(x + -1.630988787) = 4.087239612

Calculate the square root of the right side: 2.021692264

Break this problem into two subproblems by setting 
(x + -1.630988787) equal to 2.021692264 and -2.021692264.

Subproblem 1

x + -1.630988787 = 2.021692264 Simplifying x + -1.630988787 = 2.021692264 Reorder the terms: -1.630988787 + x = 2.021692264 Solving -1.630988787 + x = 2.021692264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.630988787' to each side of the equation. -1.630988787 + 1.630988787 + x = 2.021692264 + 1.630988787 Combine like terms: -1.630988787 + 1.630988787 = 0.000000000 0.000000000 + x = 2.021692264 + 1.630988787 x = 2.021692264 + 1.630988787 Combine like terms: 2.021692264 + 1.630988787 = 3.652681051 x = 3.652681051 Simplifying x = 3.652681051

Subproblem 2

x + -1.630988787 = -2.021692264 Simplifying x + -1.630988787 = -2.021692264 Reorder the terms: -1.630988787 + x = -2.021692264 Solving -1.630988787 + x = -2.021692264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.630988787' to each side of the equation. -1.630988787 + 1.630988787 + x = -2.021692264 + 1.630988787 Combine like terms: -1.630988787 + 1.630988787 = 0.000000000 0.000000000 + x = -2.021692264 + 1.630988787 x = -2.021692264 + 1.630988787 Combine like terms: -2.021692264 + 1.630988787 = -0.390703477 x = -0.390703477 Simplifying x = -0.390703477

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.652681051, -0.390703477}

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