-12x^2-46x-10=0

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Solution for -12x^2-46x-10=0 equation:


Simplifying
-12x2 + -46x + -10 = 0

Reorder the terms:
-10 + -46x + -12x2 = 0

Solving
-10 + -46x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(5 + 23x + 6x2) = 0

Ignore the factor -2.

Subproblem 1

Set the factor '(5 + 23x + 6x2)' equal to zero and attempt to solve: Simplifying 5 + 23x + 6x2 = 0 Solving 5 + 23x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 3.833333333x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 3.833333333x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 3.833333333x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 3.833333333x + x2 = 0 + -0.8333333333 3.833333333x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 3.833333333x + x2 = -0.8333333333 The x term is 3.833333333x. Take half its coefficient (1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. 3.833333333x + 3.673611112 + x2 = -0.8333333333 + 3.673611112 Reorder the terms: 3.673611112 + 3.833333333x + x2 = -0.8333333333 + 3.673611112 Combine like terms: -0.8333333333 + 3.673611112 = 2.8402777787 3.673611112 + 3.833333333x + x2 = 2.8402777787 Factor a perfect square on the left side: (x + 1.916666667)(x + 1.916666667) = 2.8402777787 Calculate the square root of the right side: 1.685312368 Break this problem into two subproblems by setting (x + 1.916666667) equal to 1.685312368 and -1.685312368.

Subproblem 1

x + 1.916666667 = 1.685312368 Simplifying x + 1.916666667 = 1.685312368 Reorder the terms: 1.916666667 + x = 1.685312368 Solving 1.916666667 + x = 1.685312368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = 1.685312368 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = 1.685312368 + -1.916666667 x = 1.685312368 + -1.916666667 Combine like terms: 1.685312368 + -1.916666667 = -0.231354299 x = -0.231354299 Simplifying x = -0.231354299

Subproblem 2

x + 1.916666667 = -1.685312368 Simplifying x + 1.916666667 = -1.685312368 Reorder the terms: 1.916666667 + x = -1.685312368 Solving 1.916666667 + x = -1.685312368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = -1.685312368 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = -1.685312368 + -1.916666667 x = -1.685312368 + -1.916666667 Combine like terms: -1.685312368 + -1.916666667 = -3.601979035 x = -3.601979035 Simplifying x = -3.601979035

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.231354299, -3.601979035}

Solution

x = {-0.231354299, -3.601979035}

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