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Simplifying -24x + 6x2 = 6x + 4 Reorder the terms: -24x + 6x2 = 4 + 6x Solving -24x + 6x2 = 4 + 6x Solving for variable 'x'. Reorder the terms: -4 + -24x + -6x + 6x2 = 4 + 6x + -4 + -6x Combine like terms: -24x + -6x = -30x -4 + -30x + 6x2 = 4 + 6x + -4 + -6x Reorder the terms: -4 + -30x + 6x2 = 4 + -4 + 6x + -6x Combine like terms: 4 + -4 = 0 -4 + -30x + 6x2 = 0 + 6x + -6x -4 + -30x + 6x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -4 + -30x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -15x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -15x + 3x2)' equal to zero and attempt to solve: Simplifying -2 + -15x + 3x2 = 0 Solving -2 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -5x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -5x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -5x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -5x + x2 = 0 + 0.6666666667 -5x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -5x + x2 = 0.6666666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 0.6666666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.6666666667 + 6.25 Combine like terms: 0.6666666667 + 6.25 = 6.9166666667 6.25 + -5x + x2 = 6.9166666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.9166666667 Calculate the square root of the right side: 2.62995564 Break this problem into two subproblems by setting (x + -2.5) equal to 2.62995564 and -2.62995564.Subproblem 1
x + -2.5 = 2.62995564 Simplifying x + -2.5 = 2.62995564 Reorder the terms: -2.5 + x = 2.62995564 Solving -2.5 + x = 2.62995564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.62995564 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.62995564 + 2.5 x = 2.62995564 + 2.5 Combine like terms: 2.62995564 + 2.5 = 5.12995564 x = 5.12995564 Simplifying x = 5.12995564Subproblem 2
x + -2.5 = -2.62995564 Simplifying x + -2.5 = -2.62995564 Reorder the terms: -2.5 + x = -2.62995564 Solving -2.5 + x = -2.62995564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.62995564 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.62995564 + 2.5 x = -2.62995564 + 2.5 Combine like terms: -2.62995564 + 2.5 = -0.12995564 x = -0.12995564 Simplifying x = -0.12995564Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.12995564, -0.12995564}Solution
x = {5.12995564, -0.12995564}
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