x^2-1.75*x-175=0

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Solution for x^2-1.75*x-175=0 equation:


Simplifying
x2 + -1.75x + -175 = 0

Reorder the terms:
-175 + -1.75x + x2 = 0

Solving
-175 + -1.75x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '175' to each side of the equation.
-175 + -1.75x + 175 + x2 = 0 + 175

Reorder the terms:
-175 + 175 + -1.75x + x2 = 0 + 175

Combine like terms: -175 + 175 = 0
0 + -1.75x + x2 = 0 + 175
-1.75x + x2 = 0 + 175

Combine like terms: 0 + 175 = 175
-1.75x + x2 = 175

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 175 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 175 + 0.765625

Combine like terms: 175 + 0.765625 = 175.765625
0.765625 + -1.75x + x2 = 175.765625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 175.765625

Calculate the square root of the right side: 13.257662879

Break this problem into two subproblems by setting 
(x + -0.875) equal to 13.257662879 and -13.257662879.

Subproblem 1

x + -0.875 = 13.257662879 Simplifying x + -0.875 = 13.257662879 Reorder the terms: -0.875 + x = 13.257662879 Solving -0.875 + x = 13.257662879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 13.257662879 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 13.257662879 + 0.875 x = 13.257662879 + 0.875 Combine like terms: 13.257662879 + 0.875 = 14.132662879 x = 14.132662879 Simplifying x = 14.132662879

Subproblem 2

x + -0.875 = -13.257662879 Simplifying x + -0.875 = -13.257662879 Reorder the terms: -0.875 + x = -13.257662879 Solving -0.875 + x = -13.257662879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -13.257662879 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -13.257662879 + 0.875 x = -13.257662879 + 0.875 Combine like terms: -13.257662879 + 0.875 = -12.382662879 x = -12.382662879 Simplifying x = -12.382662879

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.132662879, -12.382662879}

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