-16x^2+96x+120=0

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Solution for -16x^2+96x+120=0 equation:


Simplifying
-16x2 + 96x + 120 = 0

Reorder the terms:
120 + 96x + -16x2 = 0

Solving
120 + 96x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(15 + 12x + -2x2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(15 + 12x + -2x2)' equal to zero and attempt to solve: Simplifying 15 + 12x + -2x2 = 0 Solving 15 + 12x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + -6x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -6x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -6x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -6x + x2 = 0 + 7.5 -6x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -6x + x2 = 7.5 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 = 7.5 + 9 Reorder the terms: 9 + -6x + x2 = 7.5 + 9 Combine like terms: 7.5 + 9 = 16.5 9 + -6x + x2 = 16.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (x + -3) equal to 4.062019202 and -4.062019202.

Subproblem 1

x + -3 = 4.062019202 Simplifying x + -3 = 4.062019202 Reorder the terms: -3 + x = 4.062019202 Solving -3 + x = 4.062019202 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 = 4.062019202 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.062019202 + 3 x = 4.062019202 + 3 Combine like terms: 4.062019202 + 3 = 7.062019202 x = 7.062019202 Simplifying x = 7.062019202

Subproblem 2

x + -3 = -4.062019202 Simplifying x + -3 = -4.062019202 Reorder the terms: -3 + x = -4.062019202 Solving -3 + x = -4.062019202 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 = -4.062019202 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.062019202 + 3 x = -4.062019202 + 3 Combine like terms: -4.062019202 + 3 = -1.062019202 x = -1.062019202 Simplifying x = -1.062019202

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.062019202, -1.062019202}

Solution

x = {7.062019202, -1.062019202}

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