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Simplifying 2x2 + 30x + 32 = 0 Reorder the terms: 32 + 30x + 2x2 = 0 Solving 32 + 30x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + 15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + 15x + x2)' equal to zero and attempt to solve: Simplifying 16 + 15x + x2 = 0 Solving 16 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 15x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 15x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 15x + x2 = 0 + -16 15x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 15x + x2 = -16 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 = -16 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -16 + 56.25 Combine like terms: -16 + 56.25 = 40.25 56.25 + 15x + x2 = 40.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + 7.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + 7.5 = 6.34428877 Simplifying x + 7.5 = 6.34428877 Reorder the terms: 7.5 + x = 6.34428877 Solving 7.5 + x = 6.34428877 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 = 6.34428877 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 6.34428877 + -7.5 x = 6.34428877 + -7.5 Combine like terms: 6.34428877 + -7.5 = -1.15571123 x = -1.15571123 Simplifying x = -1.15571123Subproblem 2
x + 7.5 = -6.34428877 Simplifying x + 7.5 = -6.34428877 Reorder the terms: 7.5 + x = -6.34428877 Solving 7.5 + x = -6.34428877 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 = -6.34428877 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -6.34428877 + -7.5 x = -6.34428877 + -7.5 Combine like terms: -6.34428877 + -7.5 = -13.84428877 x = -13.84428877 Simplifying x = -13.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.15571123, -13.84428877}Solution
x = {-1.15571123, -13.84428877}
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