2*x^2-11*x-5+(-3)*x+(-8)*x^2=

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Solution for 2*x^2-11*x-5+(-3)*x+(-8)*x^2= equation:


Simplifying
2x2 + -11x + -5 + (-3) * x + (-8) * x2 = 0

Reorder the terms:
-5 + -11x + -3x + 2x2 + -8x2 = 0

Combine like terms: -11x + -3x = -14x
-5 + -14x + 2x2 + -8x2 = 0

Combine like terms: 2x2 + -8x2 = -6x2
-5 + -14x + -6x2 = 0

Solving
-5 + -14x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 14x + 6x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(5 + 14x + 6x2)' equal to zero and attempt to solve: Simplifying 5 + 14x + 6x2 = 0 Solving 5 + 14x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 2.333333333x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 2.333333333x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 2.333333333x + x2 = 0 + -0.8333333333 2.333333333x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 2.333333333x + x2 = -0.8333333333 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = -0.8333333333 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = -0.8333333333 + 1.361111112 Combine like terms: -0.8333333333 + 1.361111112 = 0.5277777787 1.361111112 + 2.333333333x + x2 = 0.5277777787 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 0.5277777787 Calculate the square root of the right side: 0.726483158 Break this problem into two subproblems by setting (x + 1.166666667) equal to 0.726483158 and -0.726483158.

Subproblem 1

x + 1.166666667 = 0.726483158 Simplifying x + 1.166666667 = 0.726483158 Reorder the terms: 1.166666667 + x = 0.726483158 Solving 1.166666667 + x = 0.726483158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 0.726483158 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 0.726483158 + -1.166666667 x = 0.726483158 + -1.166666667 Combine like terms: 0.726483158 + -1.166666667 = -0.440183509 x = -0.440183509 Simplifying x = -0.440183509

Subproblem 2

x + 1.166666667 = -0.726483158 Simplifying x + 1.166666667 = -0.726483158 Reorder the terms: 1.166666667 + x = -0.726483158 Solving 1.166666667 + x = -0.726483158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -0.726483158 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -0.726483158 + -1.166666667 x = -0.726483158 + -1.166666667 Combine like terms: -0.726483158 + -1.166666667 = -1.893149825 x = -1.893149825 Simplifying x = -1.893149825

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.440183509, -1.893149825}

Solution

x = {-0.440183509, -1.893149825}

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