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Simplifying 0 = -4x2 + 24x + 12 Reorder the terms: 0 = 12 + 24x + -4x2 Solving 0 = 12 + 24x + -4x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + -24x + 4x2 = 12 + 24x + -4x2 + -12 + -24x + 4x2 Reorder the terms: -12 + -24x + 4x2 = 12 + -12 + 24x + -24x + -4x2 + 4x2 Combine like terms: 12 + -12 = 0 -12 + -24x + 4x2 = 0 + 24x + -24x + -4x2 + 4x2 -12 + -24x + 4x2 = 24x + -24x + -4x2 + 4x2 Combine like terms: 24x + -24x = 0 -12 + -24x + 4x2 = 0 + -4x2 + 4x2 -12 + -24x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -12 + -24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -6x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -6x + x2)' equal to zero and attempt to solve: Simplifying -3 + -6x + x2 = 0 Solving -3 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6x + x2 = 0 + 3 -6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6x + x2 = 3 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 = 3 + 9 Reorder the terms: 9 + -6x + x2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6x + x2 = 12 Factor a perfect square on the left side: (x + -3)(x + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -3 = 3.464101615 Simplifying x + -3 = 3.464101615 Reorder the terms: -3 + x = 3.464101615 Solving -3 + x = 3.464101615 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 = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.464101615 + 3 x = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 x = 6.464101615 Simplifying x = 6.464101615Subproblem 2
x + -3 = -3.464101615 Simplifying x + -3 = -3.464101615 Reorder the terms: -3 + x = -3.464101615 Solving -3 + x = -3.464101615 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 = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.464101615 + 3 x = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 x = -0.464101615 Simplifying x = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.464101615, -0.464101615}Solution
x = {6.464101615, -0.464101615}
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