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Simplifying 16x2 + 30x + 6 = 0 Reorder the terms: 6 + 30x + 16x2 = 0 Solving 6 + 30x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 15x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 15x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 15x + 8x2 = 0 Solving 3 + 15x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 1.875x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 1.875x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 1.875x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 1.875x + x2 = 0 + -0.375 1.875x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 1.875x + x2 = -0.375 The x term is 1.875x. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875x + 0.87890625 + x2 = -0.375 + 0.87890625 Reorder the terms: 0.87890625 + 1.875x + x2 = -0.375 + 0.87890625 Combine like terms: -0.375 + 0.87890625 = 0.50390625 0.87890625 + 1.875x + x2 = 0.50390625 Factor a perfect square on the left side: (x + 0.9375)(x + 0.9375) = 0.50390625 Calculate the square root of the right side: 0.709863543 Break this problem into two subproblems by setting (x + 0.9375) equal to 0.709863543 and -0.709863543.Subproblem 1
x + 0.9375 = 0.709863543 Simplifying x + 0.9375 = 0.709863543 Reorder the terms: 0.9375 + x = 0.709863543 Solving 0.9375 + x = 0.709863543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = 0.709863543 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = 0.709863543 + -0.9375 x = 0.709863543 + -0.9375 Combine like terms: 0.709863543 + -0.9375 = -0.227636457 x = -0.227636457 Simplifying x = -0.227636457Subproblem 2
x + 0.9375 = -0.709863543 Simplifying x + 0.9375 = -0.709863543 Reorder the terms: 0.9375 + x = -0.709863543 Solving 0.9375 + x = -0.709863543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = -0.709863543 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = -0.709863543 + -0.9375 x = -0.709863543 + -0.9375 Combine like terms: -0.709863543 + -0.9375 = -1.647363543 x = -1.647363543 Simplifying x = -1.647363543Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.227636457, -1.647363543}Solution
x = {-0.227636457, -1.647363543}
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