4x^2+15x+10=0

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Solution for 4x^2+15x+10=0 equation:


Simplifying
4x2 + 15x + 10 = 0

Reorder the terms:
10 + 15x + 4x2 = 0

Solving
10 + 15x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
2.5 + 3.75x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 3.75x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 3.75x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 3.75x + x2 = 0 + -2.5
3.75x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
3.75x + x2 = -2.5

The x term is 3.75x.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75x + 3.515625 + x2 = -2.5 + 3.515625

Reorder the terms:
3.515625 + 3.75x + x2 = -2.5 + 3.515625

Combine like terms: -2.5 + 3.515625 = 1.015625
3.515625 + 3.75x + x2 = 1.015625

Factor a perfect square on the left side:
(x + 1.875)(x + 1.875) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(x + 1.875) equal to 1.007782219 and -1.007782219.

Subproblem 1

x + 1.875 = 1.007782219 Simplifying x + 1.875 = 1.007782219 Reorder the terms: 1.875 + x = 1.007782219 Solving 1.875 + x = 1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 1.007782219 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 1.007782219 + -1.875 x = 1.007782219 + -1.875 Combine like terms: 1.007782219 + -1.875 = -0.867217781 x = -0.867217781 Simplifying x = -0.867217781

Subproblem 2

x + 1.875 = -1.007782219 Simplifying x + 1.875 = -1.007782219 Reorder the terms: 1.875 + x = -1.007782219 Solving 1.875 + x = -1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -1.007782219 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -1.007782219 + -1.875 x = -1.007782219 + -1.875 Combine like terms: -1.007782219 + -1.875 = -2.882782219 x = -2.882782219 Simplifying x = -2.882782219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.867217781, -2.882782219}

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