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Simplifying 24x2 + -46x = -18 Reorder the terms: -46x + 24x2 = -18 Solving -46x + 24x2 = -18 Solving for variable 'x'. Reorder the terms: 18 + -46x + 24x2 = -18 + 18 Combine like terms: -18 + 18 = 0 18 + -46x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -23x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -23x + 12x2)' equal to zero and attempt to solve: Simplifying 9 + -23x + 12x2 = 0 Solving 9 + -23x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.75 + -1.916666667x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -1.916666667x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -1.916666667x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -1.916666667x + x2 = 0 + -0.75 -1.916666667x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -1.916666667x + x2 = -0.75 The x term is -1.916666667x. Take half its coefficient (-0.9583333335). Square it (0.9184027781) and add it to both sides. Add '0.9184027781' to each side of the equation. -1.916666667x + 0.9184027781 + x2 = -0.75 + 0.9184027781 Reorder the terms: 0.9184027781 + -1.916666667x + x2 = -0.75 + 0.9184027781 Combine like terms: -0.75 + 0.9184027781 = 0.1684027781 0.9184027781 + -1.916666667x + x2 = 0.1684027781 Factor a perfect square on the left side: (x + -0.9583333335)(x + -0.9583333335) = 0.1684027781 Calculate the square root of the right side: 0.410369075 Break this problem into two subproblems by setting (x + -0.9583333335) equal to 0.410369075 and -0.410369075.Subproblem 1
x + -0.9583333335 = 0.410369075 Simplifying x + -0.9583333335 = 0.410369075 Reorder the terms: -0.9583333335 + x = 0.410369075 Solving -0.9583333335 + x = 0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9583333335' to each side of the equation. -0.9583333335 + 0.9583333335 + x = 0.410369075 + 0.9583333335 Combine like terms: -0.9583333335 + 0.9583333335 = 0.0000000000 0.0000000000 + x = 0.410369075 + 0.9583333335 x = 0.410369075 + 0.9583333335 Combine like terms: 0.410369075 + 0.9583333335 = 1.3687024085 x = 1.3687024085 Simplifying x = 1.3687024085Subproblem 2
x + -0.9583333335 = -0.410369075 Simplifying x + -0.9583333335 = -0.410369075 Reorder the terms: -0.9583333335 + x = -0.410369075 Solving -0.9583333335 + x = -0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9583333335' to each side of the equation. -0.9583333335 + 0.9583333335 + x = -0.410369075 + 0.9583333335 Combine like terms: -0.9583333335 + 0.9583333335 = 0.0000000000 0.0000000000 + x = -0.410369075 + 0.9583333335 x = -0.410369075 + 0.9583333335 Combine like terms: -0.410369075 + 0.9583333335 = 0.5479642585 x = 0.5479642585 Simplifying x = 0.5479642585Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3687024085, 0.5479642585}Solution
x = {1.3687024085, 0.5479642585}
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