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Simplifying 2 = 4x(x + -6) Reorder the terms: 2 = 4x(-6 + x) 2 = (-6 * 4x + x * 4x) 2 = (-24x + 4x2) Solving 2 = -24x + 4x2 Solving for variable 'x'. Reorder the terms: 2 + 24x + -4x2 = -24x + 24x + 4x2 + -4x2 Combine like terms: -24x + 24x = 0 2 + 24x + -4x2 = 0 + 4x2 + -4x2 2 + 24x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 2 + 24x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 12x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 12x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + 12x + -2x2 = 0 Solving 1 + 12x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -6x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -6x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -6x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -6x + x2 = 0 + 0.5 -6x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -6x + x2 = 0.5 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 = 0.5 + 9 Reorder the terms: 9 + -6x + x2 = 0.5 + 9 Combine like terms: 0.5 + 9 = 9.5 9 + -6x + x2 = 9.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + -3) equal to 3.082207001 and -3.082207001.Subproblem 1
x + -3 = 3.082207001 Simplifying x + -3 = 3.082207001 Reorder the terms: -3 + x = 3.082207001 Solving -3 + x = 3.082207001 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 = 3.082207001 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.082207001 + 3 x = 3.082207001 + 3 Combine like terms: 3.082207001 + 3 = 6.082207001 x = 6.082207001 Simplifying x = 6.082207001Subproblem 2
x + -3 = -3.082207001 Simplifying x + -3 = -3.082207001 Reorder the terms: -3 + x = -3.082207001 Solving -3 + x = -3.082207001 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 = -3.082207001 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.082207001 + 3 x = -3.082207001 + 3 Combine like terms: -3.082207001 + 3 = -0.082207001 x = -0.082207001 Simplifying x = -0.082207001Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.082207001, -0.082207001}Solution
x = {6.082207001, -0.082207001}
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