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Simplifying 4((x2) + -6x + 9) = 192 4(x2 + -6x + 9) = 192 Reorder the terms: 4(9 + -6x + x2) = 192 (9 * 4 + -6x * 4 + x2 * 4) = 192 (36 + -24x + 4x2) = 192 Solving 36 + -24x + 4x2 = 192 Solving for variable 'x'. Reorder the terms: 36 + -192 + -24x + 4x2 = 192 + -192 Combine like terms: 36 + -192 = -156 -156 + -24x + 4x2 = 192 + -192 Combine like terms: 192 + -192 = 0 -156 + -24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-39 + -6x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-39 + -6x + x2)' equal to zero and attempt to solve: Simplifying -39 + -6x + x2 = 0 Solving -39 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -6x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -6x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -6x + x2 = 0 + 39 -6x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -6x + x2 = 39 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 = 39 + 9 Reorder the terms: 9 + -6x + x2 = 39 + 9 Combine like terms: 39 + 9 = 48 9 + -6x + x2 = 48 Factor a perfect square on the left side: (x + -3)(x + -3) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + -3) equal to 6.92820323 and -6.92820323.Subproblem 1
x + -3 = 6.92820323 Simplifying x + -3 = 6.92820323 Reorder the terms: -3 + x = 6.92820323 Solving -3 + x = 6.92820323 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 = 6.92820323 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.92820323 + 3 x = 6.92820323 + 3 Combine like terms: 6.92820323 + 3 = 9.92820323 x = 9.92820323 Simplifying x = 9.92820323Subproblem 2
x + -3 = -6.92820323 Simplifying x + -3 = -6.92820323 Reorder the terms: -3 + x = -6.92820323 Solving -3 + x = -6.92820323 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 = -6.92820323 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.92820323 + 3 x = -6.92820323 + 3 Combine like terms: -6.92820323 + 3 = -3.92820323 x = -3.92820323 Simplifying x = -3.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.92820323, -3.92820323}Solution
x = {9.92820323, -3.92820323}
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