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Simplifying 2x2 + 30x + -384 = 0 Reorder the terms: -384 + 30x + 2x2 = 0 Solving -384 + 30x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-192 + 15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-192 + 15x + x2)' equal to zero and attempt to solve: Simplifying -192 + 15x + x2 = 0 Solving -192 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + 15x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 15x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 15x + x2 = 0 + 192 15x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 15x + x2 = 192 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 192 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 192 + 56.25 Combine like terms: 192 + 56.25 = 248.25 56.25 + 15x + x2 = 248.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 248.25 Calculate the square root of the right side: 15.755951257 Break this problem into two subproblems by setting (x + 7.5) equal to 15.755951257 and -15.755951257.Subproblem 1
x + 7.5 = 15.755951257 Simplifying x + 7.5 = 15.755951257 Reorder the terms: 7.5 + x = 15.755951257 Solving 7.5 + x = 15.755951257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 15.755951257 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 15.755951257 + -7.5 x = 15.755951257 + -7.5 Combine like terms: 15.755951257 + -7.5 = 8.255951257 x = 8.255951257 Simplifying x = 8.255951257Subproblem 2
x + 7.5 = -15.755951257 Simplifying x + 7.5 = -15.755951257 Reorder the terms: 7.5 + x = -15.755951257 Solving 7.5 + x = -15.755951257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -15.755951257 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -15.755951257 + -7.5 x = -15.755951257 + -7.5 Combine like terms: -15.755951257 + -7.5 = -23.255951257 x = -23.255951257 Simplifying x = -23.255951257Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.255951257, -23.255951257}Solution
x = {8.255951257, -23.255951257}
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