-4.9x^2+280x+115=0

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Solution for -4.9x^2+280x+115=0 equation:


Simplifying
-4.9x2 + 280x + 115 = 0

Reorder the terms:
115 + 280x + -4.9x2 = 0

Solving
115 + 280x + -4.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '-4.9'.
-23.46938776 + -57.14285714x + x2 = 0

Move the constant term to the right:

Add '23.46938776' to each side of the equation.
-23.46938776 + -57.14285714x + 23.46938776 + x2 = 0 + 23.46938776

Reorder the terms:
-23.46938776 + 23.46938776 + -57.14285714x + x2 = 0 + 23.46938776

Combine like terms: -23.46938776 + 23.46938776 = 0.00000000
0.00000000 + -57.14285714x + x2 = 0 + 23.46938776
-57.14285714x + x2 = 0 + 23.46938776

Combine like terms: 0 + 23.46938776 = 23.46938776
-57.14285714x + x2 = 23.46938776

The x term is -57.14285714x.  Take half its coefficient (-28.57142857).
Square it (816.3265305) and add it to both sides.

Add '816.3265305' to each side of the equation.
-57.14285714x + 816.3265305 + x2 = 23.46938776 + 816.3265305

Reorder the terms:
816.3265305 + -57.14285714x + x2 = 23.46938776 + 816.3265305

Combine like terms: 23.46938776 + 816.3265305 = 839.79591826
816.3265305 + -57.14285714x + x2 = 839.79591826

Factor a perfect square on the left side:
(x + -28.57142857)(x + -28.57142857) = 839.79591826

Calculate the square root of the right side: 28.979232534

Break this problem into two subproblems by setting 
(x + -28.57142857) equal to 28.979232534 and -28.979232534.

Subproblem 1

x + -28.57142857 = 28.979232534 Simplifying x + -28.57142857 = 28.979232534 Reorder the terms: -28.57142857 + x = 28.979232534 Solving -28.57142857 + x = 28.979232534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.57142857' to each side of the equation. -28.57142857 + 28.57142857 + x = 28.979232534 + 28.57142857 Combine like terms: -28.57142857 + 28.57142857 = 0.00000000 0.00000000 + x = 28.979232534 + 28.57142857 x = 28.979232534 + 28.57142857 Combine like terms: 28.979232534 + 28.57142857 = 57.550661104 x = 57.550661104 Simplifying x = 57.550661104

Subproblem 2

x + -28.57142857 = -28.979232534 Simplifying x + -28.57142857 = -28.979232534 Reorder the terms: -28.57142857 + x = -28.979232534 Solving -28.57142857 + x = -28.979232534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.57142857' to each side of the equation. -28.57142857 + 28.57142857 + x = -28.979232534 + 28.57142857 Combine like terms: -28.57142857 + 28.57142857 = 0.00000000 0.00000000 + x = -28.979232534 + 28.57142857 x = -28.979232534 + 28.57142857 Combine like terms: -28.979232534 + 28.57142857 = -0.407803964 x = -0.407803964 Simplifying x = -0.407803964

Solution

The solution to the problem is based on the solutions from the subproblems. x = {57.550661104, -0.407803964}

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