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Simplifying 4x2 + 96x + -412 = 0 Reorder the terms: -412 + 96x + 4x2 = 0 Solving -412 + 96x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-103 + 24x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-103 + 24x + x2)' equal to zero and attempt to solve: Simplifying -103 + 24x + x2 = 0 Solving -103 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '103' to each side of the equation. -103 + 24x + 103 + x2 = 0 + 103 Reorder the terms: -103 + 103 + 24x + x2 = 0 + 103 Combine like terms: -103 + 103 = 0 0 + 24x + x2 = 0 + 103 24x + x2 = 0 + 103 Combine like terms: 0 + 103 = 103 24x + x2 = 103 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 103 + 144 Reorder the terms: 144 + 24x + x2 = 103 + 144 Combine like terms: 103 + 144 = 247 144 + 24x + x2 = 247 Factor a perfect square on the left side: (x + 12)(x + 12) = 247 Calculate the square root of the right side: 15.716233646 Break this problem into two subproblems by setting (x + 12) equal to 15.716233646 and -15.716233646.Subproblem 1
x + 12 = 15.716233646 Simplifying x + 12 = 15.716233646 Reorder the terms: 12 + x = 15.716233646 Solving 12 + x = 15.716233646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 15.716233646 + -12 Combine like terms: 12 + -12 = 0 0 + x = 15.716233646 + -12 x = 15.716233646 + -12 Combine like terms: 15.716233646 + -12 = 3.716233646 x = 3.716233646 Simplifying x = 3.716233646Subproblem 2
x + 12 = -15.716233646 Simplifying x + 12 = -15.716233646 Reorder the terms: 12 + x = -15.716233646 Solving 12 + x = -15.716233646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -15.716233646 + -12 Combine like terms: 12 + -12 = 0 0 + x = -15.716233646 + -12 x = -15.716233646 + -12 Combine like terms: -15.716233646 + -12 = -27.716233646 x = -27.716233646 Simplifying x = -27.716233646Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.716233646, -27.716233646}Solution
x = {3.716233646, -27.716233646}
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