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Simplifying 8x2 + 30x + 16 = 0 Reorder the terms: 16 + 30x + 8x2 = 0 Solving 16 + 30x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 15x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + 15x + 4x2)' equal to zero and attempt to solve: Simplifying 8 + 15x + 4x2 = 0 Solving 8 + 15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + 3.75x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.75x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3.75x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.75x + x2 = 0 + -2 3.75x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.75x + x2 = -2 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = -2 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = -2 + 3.515625 Combine like terms: -2 + 3.515625 = 1.515625 3.515625 + 3.75x + x2 = 1.515625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + 1.875) equal to 1.231107225 and -1.231107225.Subproblem 1
x + 1.875 = 1.231107225 Simplifying x + 1.875 = 1.231107225 Reorder the terms: 1.875 + x = 1.231107225 Solving 1.875 + x = 1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 1.231107225 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 1.231107225 + -1.875 x = 1.231107225 + -1.875 Combine like terms: 1.231107225 + -1.875 = -0.643892775 x = -0.643892775 Simplifying x = -0.643892775Subproblem 2
x + 1.875 = -1.231107225 Simplifying x + 1.875 = -1.231107225 Reorder the terms: 1.875 + x = -1.231107225 Solving 1.875 + x = -1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -1.231107225 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -1.231107225 + -1.875 x = -1.231107225 + -1.875 Combine like terms: -1.231107225 + -1.875 = -3.106107225 x = -3.106107225 Simplifying x = -3.106107225Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.643892775, -3.106107225}Solution
x = {-0.643892775, -3.106107225}
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