30x^2-70x-500=0

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Solution for 30x^2-70x-500=0 equation:


Simplifying
30x2 + -70x + -500 = 0

Reorder the terms:
-500 + -70x + 30x2 = 0

Solving
-500 + -70x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-50 + -7x + 3x2) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(-50 + -7x + 3x2)' equal to zero and attempt to solve: Simplifying -50 + -7x + 3x2 = 0 Solving -50 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.66666667 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + -2.333333333x + 16.66666667 + x2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + -2.333333333x + x2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + -2.333333333x + x2 = 0 + 16.66666667 -2.333333333x + x2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 -2.333333333x + x2 = 16.66666667 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 = 16.66666667 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 16.66666667 + 1.361111112 Combine like terms: 16.66666667 + 1.361111112 = 18.027777782 1.361111112 + -2.333333333x + x2 = 18.027777782 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 18.027777782 Calculate the square root of the right side: 4.245913068 Break this problem into two subproblems by setting (x + -1.166666667) equal to 4.245913068 and -4.245913068.

Subproblem 1

x + -1.166666667 = 4.245913068 Simplifying x + -1.166666667 = 4.245913068 Reorder the terms: -1.166666667 + x = 4.245913068 Solving -1.166666667 + x = 4.245913068 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 = 4.245913068 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 4.245913068 + 1.166666667 x = 4.245913068 + 1.166666667 Combine like terms: 4.245913068 + 1.166666667 = 5.412579735 x = 5.412579735 Simplifying x = 5.412579735

Subproblem 2

x + -1.166666667 = -4.245913068 Simplifying x + -1.166666667 = -4.245913068 Reorder the terms: -1.166666667 + x = -4.245913068 Solving -1.166666667 + x = -4.245913068 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 = -4.245913068 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -4.245913068 + 1.166666667 x = -4.245913068 + 1.166666667 Combine like terms: -4.245913068 + 1.166666667 = -3.079246401 x = -3.079246401 Simplifying x = -3.079246401

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.412579735, -3.079246401}

Solution

x = {5.412579735, -3.079246401}

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