4x^2+5x=280

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Solution for 4x^2+5x=280 equation:


Simplifying
4x2 + 5x = 280

Reorder the terms:
5x + 4x2 = 280

Solving
5x + 4x2 = 280

Solving for variable 'x'.

Reorder the terms:
-280 + 5x + 4x2 = 280 + -280

Combine like terms: 280 + -280 = 0
-280 + 5x + 4x2 = 0

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

Divide each side by '4'.
-70 + 1.25x + x2 = 0

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 1.25x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 1.25x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 1.25x + x2 = 0 + 70
1.25x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
1.25x + x2 = 70

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 70 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 70 + 0.390625

Combine like terms: 70 + 0.390625 = 70.390625
0.390625 + 1.25x + x2 = 70.390625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 70.390625

Calculate the square root of the right side: 8.389912097

Break this problem into two subproblems by setting 
(x + 0.625) equal to 8.389912097 and -8.389912097.

Subproblem 1

x + 0.625 = 8.389912097 Simplifying x + 0.625 = 8.389912097 Reorder the terms: 0.625 + x = 8.389912097 Solving 0.625 + x = 8.389912097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 8.389912097 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 8.389912097 + -0.625 x = 8.389912097 + -0.625 Combine like terms: 8.389912097 + -0.625 = 7.764912097 x = 7.764912097 Simplifying x = 7.764912097

Subproblem 2

x + 0.625 = -8.389912097 Simplifying x + 0.625 = -8.389912097 Reorder the terms: 0.625 + x = -8.389912097 Solving 0.625 + x = -8.389912097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -8.389912097 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -8.389912097 + -0.625 x = -8.389912097 + -0.625 Combine like terms: -8.389912097 + -0.625 = -9.014912097 x = -9.014912097 Simplifying x = -9.014912097

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.764912097, -9.014912097}

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