-4x^2-10x+3=0

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Solution for -4x^2-10x+3=0 equation:


Simplifying
-4x2 + -10x + 3 = 0

Reorder the terms:
3 + -10x + -4x2 = 0

Solving
3 + -10x + -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'.
-0.75 + 2.5x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 2.5x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 2.5x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 2.5x + x2 = 0 + 0.75
2.5x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
2.5x + x2 = 0.75

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 0.75 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 0.75 + 1.5625

Combine like terms: 0.75 + 1.5625 = 2.3125
1.5625 + 2.5x + x2 = 2.3125

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 2.3125

Calculate the square root of the right side: 1.520690633

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.520690633 and -1.520690633.

Subproblem 1

x + 1.25 = 1.520690633 Simplifying x + 1.25 = 1.520690633 Reorder the terms: 1.25 + x = 1.520690633 Solving 1.25 + x = 1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.520690633 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.520690633 + -1.25 x = 1.520690633 + -1.25 Combine like terms: 1.520690633 + -1.25 = 0.270690633 x = 0.270690633 Simplifying x = 0.270690633

Subproblem 2

x + 1.25 = -1.520690633 Simplifying x + 1.25 = -1.520690633 Reorder the terms: 1.25 + x = -1.520690633 Solving 1.25 + x = -1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.520690633 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.520690633 + -1.25 x = -1.520690633 + -1.25 Combine like terms: -1.520690633 + -1.25 = -2.770690633 x = -2.770690633 Simplifying x = -2.770690633

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.270690633, -2.770690633}

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