-30x^2+80x+10=0

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Solution for -30x^2+80x+10=0 equation:


Simplifying
-30x2 + 80x + 10 = 0

Reorder the terms:
10 + 80x + -30x2 = 0

Solving
10 + 80x + -30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + 8x + -3x2) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(1 + 8x + -3x2)' equal to zero and attempt to solve: Simplifying 1 + 8x + -3x2 = 0 Solving 1 + 8x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.3333333333 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -2.666666667x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -2.666666667x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -2.666666667x + x2 = 0 + 0.3333333333 -2.666666667x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -2.666666667x + x2 = 0.3333333333 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 0.3333333333 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 0.3333333333 + 1.777777780 Combine like terms: 0.3333333333 + 1.777777780 = 2.1111111133 1.777777780 + -2.666666667x + x2 = 2.1111111133 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 2.1111111133 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.452966315 and -1.452966315.

Subproblem 1

x + -1.333333334 = 1.452966315 Simplifying x + -1.333333334 = 1.452966315 Reorder the terms: -1.333333334 + x = 1.452966315 Solving -1.333333334 + x = 1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.452966315 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.452966315 + 1.333333334 x = 1.452966315 + 1.333333334 Combine like terms: 1.452966315 + 1.333333334 = 2.786299649 x = 2.786299649 Simplifying x = 2.786299649

Subproblem 2

x + -1.333333334 = -1.452966315 Simplifying x + -1.333333334 = -1.452966315 Reorder the terms: -1.333333334 + x = -1.452966315 Solving -1.333333334 + x = -1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.452966315 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.452966315 + 1.333333334 x = -1.452966315 + 1.333333334 Combine like terms: -1.452966315 + 1.333333334 = -0.119632981 x = -0.119632981 Simplifying x = -0.119632981

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.786299649, -0.119632981}

Solution

x = {2.786299649, -0.119632981}

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