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Simplifying 24x2 + 46x = 10 Reorder the terms: 46x + 24x2 = 10 Solving 46x + 24x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 46x + 24x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 46x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 23x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 23x + 12x2)' equal to zero and attempt to solve: Simplifying -5 + 23x + 12x2 = 0 Solving -5 + 23x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + 1.916666667x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + 1.916666667x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + 1.916666667x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + 1.916666667x + x2 = 0 + 0.4166666667 1.916666667x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 1.916666667x + x2 = 0.4166666667 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 = 0.4166666667 + 0.9184027781 Reorder the terms: 0.9184027781 + 1.916666667x + x2 = 0.4166666667 + 0.9184027781 Combine like terms: 0.4166666667 + 0.9184027781 = 1.3350694448 0.9184027781 + 1.916666667x + x2 = 1.3350694448 Factor a perfect square on the left side: (x + 0.9583333335)(x + 0.9583333335) = 1.3350694448 Calculate the square root of the right side: 1.155452052 Break this problem into two subproblems by setting (x + 0.9583333335) equal to 1.155452052 and -1.155452052.Subproblem 1
x + 0.9583333335 = 1.155452052 Simplifying x + 0.9583333335 = 1.155452052 Reorder the terms: 0.9583333335 + x = 1.155452052 Solving 0.9583333335 + x = 1.155452052 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 = 1.155452052 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = 1.155452052 + -0.9583333335 x = 1.155452052 + -0.9583333335 Combine like terms: 1.155452052 + -0.9583333335 = 0.1971187185 x = 0.1971187185 Simplifying x = 0.1971187185Subproblem 2
x + 0.9583333335 = -1.155452052 Simplifying x + 0.9583333335 = -1.155452052 Reorder the terms: 0.9583333335 + x = -1.155452052 Solving 0.9583333335 + x = -1.155452052 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 = -1.155452052 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = -1.155452052 + -0.9583333335 x = -1.155452052 + -0.9583333335 Combine like terms: -1.155452052 + -0.9583333335 = -2.1137853855 x = -2.1137853855 Simplifying x = -2.1137853855Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1971187185, -2.1137853855}Solution
x = {0.1971187185, -2.1137853855}
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