-3x^2+5x-1=-7

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Solution for -3x^2+5x-1=-7 equation:


Simplifying
-3x2 + 5x + -1 = -7

Reorder the terms:
-1 + 5x + -3x2 = -7

Solving
-1 + 5x + -3x2 = -7

Solving for variable 'x'.

Reorder the terms:
-1 + 7 + 5x + -3x2 = -7 + 7

Combine like terms: -1 + 7 = 6
6 + 5x + -3x2 = -7 + 7

Combine like terms: -7 + 7 = 0
6 + 5x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-2 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -1.666666667x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -1.666666667x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1.666666667x + x2 = 0 + 2
-1.666666667x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1.666666667x + x2 = 2

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 2 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 2 + 0.6944444447

Combine like terms: 2 + 0.6944444447 = 2.6944444447
0.6944444447 + -1.666666667x + x2 = 2.6944444447

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 2.6944444447

Calculate the square root of the right side: 1.6414763

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 1.6414763 and -1.6414763.

Subproblem 1

x + -0.8333333335 = 1.6414763 Simplifying x + -0.8333333335 = 1.6414763 Reorder the terms: -0.8333333335 + x = 1.6414763 Solving -0.8333333335 + x = 1.6414763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.6414763 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.6414763 + 0.8333333335 x = 1.6414763 + 0.8333333335 Combine like terms: 1.6414763 + 0.8333333335 = 2.4748096335 x = 2.4748096335 Simplifying x = 2.4748096335

Subproblem 2

x + -0.8333333335 = -1.6414763 Simplifying x + -0.8333333335 = -1.6414763 Reorder the terms: -0.8333333335 + x = -1.6414763 Solving -0.8333333335 + x = -1.6414763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.6414763 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.6414763 + 0.8333333335 x = -1.6414763 + 0.8333333335 Combine like terms: -1.6414763 + 0.8333333335 = -0.8081429665 x = -0.8081429665 Simplifying x = -0.8081429665

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.4748096335, -0.8081429665}

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