-3x^2+18x=-30

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Solution for -3x^2+18x=-30 equation:


Simplifying
-3x2 + 18x = -30

Reorder the terms:
18x + -3x2 = -30

Solving
18x + -3x2 = -30

Solving for variable 'x'.

Reorder the terms:
30 + 18x + -3x2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + 18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + 6x + -1x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(10 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 10 + 6x + -1x2 = 0 Solving 10 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -6x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -6x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -6x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -6x + x2 = 0 + 10 -6x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -6x + x2 = 10 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 10 + 9 Reorder the terms: 9 + -6x + x2 = 10 + 9 Combine like terms: 10 + 9 = 19 9 + -6x + x2 = 19 Factor a perfect square on the left side: (x + -3)(x + -3) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -3) equal to 4.358898944 and -4.358898944.

Subproblem 1

x + -3 = 4.358898944 Simplifying x + -3 = 4.358898944 Reorder the terms: -3 + x = 4.358898944 Solving -3 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.358898944 + 3 x = 4.358898944 + 3 Combine like terms: 4.358898944 + 3 = 7.358898944 x = 7.358898944 Simplifying x = 7.358898944

Subproblem 2

x + -3 = -4.358898944 Simplifying x + -3 = -4.358898944 Reorder the terms: -3 + x = -4.358898944 Solving -3 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.358898944 + 3 x = -4.358898944 + 3 Combine like terms: -4.358898944 + 3 = -1.358898944 x = -1.358898944 Simplifying x = -1.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.358898944, -1.358898944}

Solution

x = {7.358898944, -1.358898944}

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