1x^2-2.5x=10

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Solution for 1x^2-2.5x=10 equation:


Simplifying
1x2 + -2.5x = 10

Reorder the terms:
-2.5x + 1x2 = 10

Solving
-2.5x + 1x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -2.5x + 1x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -2.5x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2.5x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -2.5x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2.5x + x2 = 0 + 10
-2.5x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2.5x + x2 = 10

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 = 10 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 10 + 1.5625

Combine like terms: 10 + 1.5625 = 11.5625
1.5625 + -2.5x + x2 = 11.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 11.5625

Calculate the square root of the right side: 3.400367627

Break this problem into two subproblems by setting 
(x + -1.25) equal to 3.400367627 and -3.400367627.

Subproblem 1

x + -1.25 = 3.400367627 Simplifying x + -1.25 = 3.400367627 Reorder the terms: -1.25 + x = 3.400367627 Solving -1.25 + x = 3.400367627 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 = 3.400367627 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.400367627 + 1.25 x = 3.400367627 + 1.25 Combine like terms: 3.400367627 + 1.25 = 4.650367627 x = 4.650367627 Simplifying x = 4.650367627

Subproblem 2

x + -1.25 = -3.400367627 Simplifying x + -1.25 = -3.400367627 Reorder the terms: -1.25 + x = -3.400367627 Solving -1.25 + x = -3.400367627 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 = -3.400367627 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.400367627 + 1.25 x = -3.400367627 + 1.25 Combine like terms: -3.400367627 + 1.25 = -2.150367627 x = -2.150367627 Simplifying x = -2.150367627

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.650367627, -2.150367627}

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