15=4x^2+12.5x+9.75

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Solution for 15=4x^2+12.5x+9.75 equation:


Simplifying
15 = 4x2 + 12.5x + 9.75

Reorder the terms:
15 = 9.75 + 12.5x + 4x2

Solving
15 = 9.75 + 12.5x + 4x2

Solving for variable 'x'.

Combine like terms: 15 + -9.75 = 5.25
5.25 + -12.5x + -4x2 = 9.75 + 12.5x + 4x2 + -9.75 + -12.5x + -4x2

Reorder the terms:
5.25 + -12.5x + -4x2 = 9.75 + -9.75 + 12.5x + -12.5x + 4x2 + -4x2

Combine like terms: 9.75 + -9.75 = 0.00
5.25 + -12.5x + -4x2 = 0.00 + 12.5x + -12.5x + 4x2 + -4x2
5.25 + -12.5x + -4x2 = 12.5x + -12.5x + 4x2 + -4x2

Combine like terms: 12.5x + -12.5x = 0.0
5.25 + -12.5x + -4x2 = 0.0 + 4x2 + -4x2
5.25 + -12.5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
5.25 + -12.5x + -4x2 = 0

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

Divide each side by '-4'.
-1.3125 + 3.125x + x2 = 0

Move the constant term to the right:

Add '1.3125' to each side of the equation.
-1.3125 + 3.125x + 1.3125 + x2 = 0 + 1.3125

Reorder the terms:
-1.3125 + 1.3125 + 3.125x + x2 = 0 + 1.3125

Combine like terms: -1.3125 + 1.3125 = 0.0000
0.0000 + 3.125x + x2 = 0 + 1.3125
3.125x + x2 = 0 + 1.3125

Combine like terms: 0 + 1.3125 = 1.3125
3.125x + x2 = 1.3125

The x term is 3.125x.  Take half its coefficient (1.5625).
Square it (2.44140625) and add it to both sides.

Add '2.44140625' to each side of the equation.
3.125x + 2.44140625 + x2 = 1.3125 + 2.44140625

Reorder the terms:
2.44140625 + 3.125x + x2 = 1.3125 + 2.44140625

Combine like terms: 1.3125 + 2.44140625 = 3.75390625
2.44140625 + 3.125x + x2 = 3.75390625

Factor a perfect square on the left side:
(x + 1.5625)(x + 1.5625) = 3.75390625

Calculate the square root of the right side: 1.9375

Break this problem into two subproblems by setting 
(x + 1.5625) equal to 1.9375 and -1.9375.

Subproblem 1

x + 1.5625 = 1.9375 Simplifying x + 1.5625 = 1.9375 Reorder the terms: 1.5625 + x = 1.9375 Solving 1.5625 + x = 1.9375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = 1.9375 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = 1.9375 + -1.5625 x = 1.9375 + -1.5625 Combine like terms: 1.9375 + -1.5625 = 0.375 x = 0.375 Simplifying x = 0.375

Subproblem 2

x + 1.5625 = -1.9375 Simplifying x + 1.5625 = -1.9375 Reorder the terms: 1.5625 + x = -1.9375 Solving 1.5625 + x = -1.9375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = -1.9375 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = -1.9375 + -1.5625 x = -1.9375 + -1.5625 Combine like terms: -1.9375 + -1.5625 = -3.5 x = -3.5 Simplifying x = -3.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.375, -3.5}

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