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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 + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying -3 + 6x + -1x2 = 0 Solving -3 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -6x + x2 = 0 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 = 6 9 + -6x + x2 = 6 Factor a perfect square on the left side: (x + -3)(x + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -3 = 2.449489743 Simplifying x + -3 = 2.449489743 Reorder the terms: -3 + x = 2.449489743 Solving -3 + x = 2.449489743 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 = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.449489743 + 3 x = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 x = 5.449489743 Simplifying x = 5.449489743Subproblem 2
x + -3 = -2.449489743 Simplifying x + -3 = -2.449489743 Reorder the terms: -3 + x = -2.449489743 Solving -3 + x = -2.449489743 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 = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.449489743 + 3 x = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 x = 0.550510257 Simplifying x = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.449489743, 0.550510257}Solution
x = {5.449489743, 0.550510257}
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