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Simplifying 24x2 + 63x + 15 = 0 Reorder the terms: 15 + 63x + 24x2 = 0 Solving 15 + 63x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 21x + 8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 21x + 8x2)' equal to zero and attempt to solve: Simplifying 5 + 21x + 8x2 = 0 Solving 5 + 21x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 2.625x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 2.625x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 2.625x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 2.625x + x2 = 0 + -0.625 2.625x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 2.625x + x2 = -0.625 The x term is 2.625x. Take half its coefficient (1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. 2.625x + 1.72265625 + x2 = -0.625 + 1.72265625 Reorder the terms: 1.72265625 + 2.625x + x2 = -0.625 + 1.72265625 Combine like terms: -0.625 + 1.72265625 = 1.09765625 1.72265625 + 2.625x + x2 = 1.09765625 Factor a perfect square on the left side: (x + 1.3125)(x + 1.3125) = 1.09765625 Calculate the square root of the right side: 1.047690913 Break this problem into two subproblems by setting (x + 1.3125) equal to 1.047690913 and -1.047690913.Subproblem 1
x + 1.3125 = 1.047690913 Simplifying x + 1.3125 = 1.047690913 Reorder the terms: 1.3125 + x = 1.047690913 Solving 1.3125 + x = 1.047690913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + x = 1.047690913 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = 1.047690913 + -1.3125 x = 1.047690913 + -1.3125 Combine like terms: 1.047690913 + -1.3125 = -0.264809087 x = -0.264809087 Simplifying x = -0.264809087Subproblem 2
x + 1.3125 = -1.047690913 Simplifying x + 1.3125 = -1.047690913 Reorder the terms: 1.3125 + x = -1.047690913 Solving 1.3125 + x = -1.047690913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + x = -1.047690913 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = -1.047690913 + -1.3125 x = -1.047690913 + -1.3125 Combine like terms: -1.047690913 + -1.3125 = -2.360190913 x = -2.360190913 Simplifying x = -2.360190913Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.264809087, -2.360190913}Solution
x = {-0.264809087, -2.360190913}
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