0=-4.9x^2+39.2x+7

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Solution for 0=-4.9x^2+39.2x+7 equation:


Simplifying
0 = -4.9x2 + 39.2x + 7

Reorder the terms:
0 = 7 + 39.2x + -4.9x2

Solving
0 = 7 + 39.2x + -4.9x2

Solving for variable 'x'.

Combine like terms: 0 + -7 = -7
-7 + -39.2x + 4.9x2 = 7 + 39.2x + -4.9x2 + -7 + -39.2x + 4.9x2

Reorder the terms:
-7 + -39.2x + 4.9x2 = 7 + -7 + 39.2x + -39.2x + -4.9x2 + 4.9x2

Combine like terms: 7 + -7 = 0
-7 + -39.2x + 4.9x2 = 0 + 39.2x + -39.2x + -4.9x2 + 4.9x2
-7 + -39.2x + 4.9x2 = 39.2x + -39.2x + -4.9x2 + 4.9x2

Combine like terms: 39.2x + -39.2x = 0.0
-7 + -39.2x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2
-7 + -39.2x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
-7 + -39.2x + 4.9x2 = 0.0

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

Divide each side by '4.9'.
-1.428571429 + -8x + x2 = 0

Move the constant term to the right:

Add '1.428571429' to each side of the equation.
-1.428571429 + -8x + 1.428571429 + x2 = 0 + 1.428571429

Reorder the terms:
-1.428571429 + 1.428571429 + -8x + x2 = 0 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + -8x + x2 = 0 + 1.428571429
-8x + x2 = 0 + 1.428571429

Combine like terms: 0 + 1.428571429 = 1.428571429
-8x + x2 = 1.428571429

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 1.428571429 + 16

Reorder the terms:
16 + -8x + x2 = 1.428571429 + 16

Combine like terms: 1.428571429 + 16 = 17.428571429
16 + -8x + x2 = 17.428571429

Factor a perfect square on the left side:
(x + -4)(x + -4) = 17.428571429

Calculate the square root of the right side: 4.174754056

Break this problem into two subproblems by setting 
(x + -4) equal to 4.174754056 and -4.174754056.

Subproblem 1

x + -4 = 4.174754056 Simplifying x + -4 = 4.174754056 Reorder the terms: -4 + x = 4.174754056 Solving -4 + x = 4.174754056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.174754056 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.174754056 + 4 x = 4.174754056 + 4 Combine like terms: 4.174754056 + 4 = 8.174754056 x = 8.174754056 Simplifying x = 8.174754056

Subproblem 2

x + -4 = -4.174754056 Simplifying x + -4 = -4.174754056 Reorder the terms: -4 + x = -4.174754056 Solving -4 + x = -4.174754056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.174754056 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.174754056 + 4 x = -4.174754056 + 4 Combine like terms: -4.174754056 + 4 = -0.174754056 x = -0.174754056 Simplifying x = -0.174754056

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.174754056, -0.174754056}

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