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Simplifying 0 = 24x2 + 15x + -3 Reorder the terms: 0 = -3 + 15x + 24x2 Solving 0 = -3 + 15x + 24x2 Solving for variable 'x'. Combine like terms: 0 + 3 = 3 3 + -15x + -24x2 = -3 + 15x + 24x2 + 3 + -15x + -24x2 Reorder the terms: 3 + -15x + -24x2 = -3 + 3 + 15x + -15x + 24x2 + -24x2 Combine like terms: -3 + 3 = 0 3 + -15x + -24x2 = 0 + 15x + -15x + 24x2 + -24x2 3 + -15x + -24x2 = 15x + -15x + 24x2 + -24x2 Combine like terms: 15x + -15x = 0 3 + -15x + -24x2 = 0 + 24x2 + -24x2 3 + -15x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 3 + -15x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -5x + -8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -5x + -8x2)' equal to zero and attempt to solve: Simplifying 1 + -5x + -8x2 = 0 Solving 1 + -5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + 0.625x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.625x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.625x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.625x + x2 = 0 + 0.125 0.625x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.625x + x2 = 0.125 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 0.125 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 0.125 + 0.09765625 Combine like terms: 0.125 + 0.09765625 = 0.22265625 0.09765625 + 0.625x + x2 = 0.22265625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (x + 0.3125) equal to 0.471864652 and -0.471864652.Subproblem 1
x + 0.3125 = 0.471864652 Simplifying x + 0.3125 = 0.471864652 Reorder the terms: 0.3125 + x = 0.471864652 Solving 0.3125 + x = 0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 0.471864652 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 0.471864652 + -0.3125 x = 0.471864652 + -0.3125 Combine like terms: 0.471864652 + -0.3125 = 0.159364652 x = 0.159364652 Simplifying x = 0.159364652Subproblem 2
x + 0.3125 = -0.471864652 Simplifying x + 0.3125 = -0.471864652 Reorder the terms: 0.3125 + x = -0.471864652 Solving 0.3125 + x = -0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -0.471864652 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -0.471864652 + -0.3125 x = -0.471864652 + -0.3125 Combine like terms: -0.471864652 + -0.3125 = -0.784364652 x = -0.784364652 Simplifying x = -0.784364652Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.159364652, -0.784364652}Solution
x = {0.159364652, -0.784364652}
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