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Simplifying -16x2 + -96x + 144 = 0 Reorder the terms: 144 + -96x + -16x2 = 0 Solving 144 + -96x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(9 + -6x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(9 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 9 + -6x + -1x2 = 0 Solving 9 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 6x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 6x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 6x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 6x + x2 = 0 + 9 6x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 6x + x2 = 9 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 = 9 + 9 Reorder the terms: 9 + 6x + x2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + 6x + x2 = 18 Factor a perfect square on the left side: (x + 3)(x + 3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 3) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 3 = 4.242640687 Simplifying x + 3 = 4.242640687 Reorder the terms: 3 + x = 4.242640687 Solving 3 + x = 4.242640687 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 = 4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.242640687 + -3 x = 4.242640687 + -3 Combine like terms: 4.242640687 + -3 = 1.242640687 x = 1.242640687 Simplifying x = 1.242640687Subproblem 2
x + 3 = -4.242640687 Simplifying x + 3 = -4.242640687 Reorder the terms: 3 + x = -4.242640687 Solving 3 + x = -4.242640687 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 = -4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.242640687 + -3 x = -4.242640687 + -3 Combine like terms: -4.242640687 + -3 = -7.242640687 x = -7.242640687 Simplifying x = -7.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.242640687, -7.242640687}Solution
x = {1.242640687, -7.242640687}
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