0.5x^2-1.2x-7=0

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Solution for 0.5x^2-1.2x-7=0 equation:


Simplifying
0.5x2 + -1.2x + -7 = 0

Reorder the terms:
-7 + -1.2x + 0.5x2 = 0

Solving
-7 + -1.2x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
-14 + -2.4x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -2.4x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -2.4x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -2.4x + x2 = 0 + 14
-2.4x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-2.4x + x2 = 14

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = 14 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = 14 + 1.44

Combine like terms: 14 + 1.44 = 15.44
1.44 + -2.4x + x2 = 15.44

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 15.44

Calculate the square root of the right side: 3.929376541

Break this problem into two subproblems by setting 
(x + -1.2) equal to 3.929376541 and -3.929376541.

Subproblem 1

x + -1.2 = 3.929376541 Simplifying x + -1.2 = 3.929376541 Reorder the terms: -1.2 + x = 3.929376541 Solving -1.2 + x = 3.929376541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 3.929376541 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 3.929376541 + 1.2 x = 3.929376541 + 1.2 Combine like terms: 3.929376541 + 1.2 = 5.129376541 x = 5.129376541 Simplifying x = 5.129376541

Subproblem 2

x + -1.2 = -3.929376541 Simplifying x + -1.2 = -3.929376541 Reorder the terms: -1.2 + x = -3.929376541 Solving -1.2 + x = -3.929376541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -3.929376541 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -3.929376541 + 1.2 x = -3.929376541 + 1.2 Combine like terms: -3.929376541 + 1.2 = -2.729376541 x = -2.729376541 Simplifying x = -2.729376541

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.129376541, -2.729376541}

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