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Simplifying 3x2 + 48x + -7 = 0 Reorder the terms: -7 + 48x + 3x2 = 0 Solving -7 + 48x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + 16x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 16x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 16x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 16x + x2 = 0 + 2.333333333 16x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 16x + x2 = 2.333333333 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 2.333333333 + 64 Reorder the terms: 64 + 16x + x2 = 2.333333333 + 64 Combine like terms: 2.333333333 + 64 = 66.333333333 64 + 16x + x2 = 66.333333333 Factor a perfect square on the left side: (x + 8)(x + 8) = 66.333333333 Calculate the square root of the right side: 8.144527815 Break this problem into two subproblems by setting (x + 8) equal to 8.144527815 and -8.144527815.Subproblem 1
x + 8 = 8.144527815 Simplifying x + 8 = 8.144527815 Reorder the terms: 8 + x = 8.144527815 Solving 8 + x = 8.144527815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 8.144527815 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.144527815 + -8 x = 8.144527815 + -8 Combine like terms: 8.144527815 + -8 = 0.144527815 x = 0.144527815 Simplifying x = 0.144527815Subproblem 2
x + 8 = -8.144527815 Simplifying x + 8 = -8.144527815 Reorder the terms: 8 + x = -8.144527815 Solving 8 + x = -8.144527815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -8.144527815 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.144527815 + -8 x = -8.144527815 + -8 Combine like terms: -8.144527815 + -8 = -16.144527815 x = -16.144527815 Simplifying x = -16.144527815Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.144527815, -16.144527815}
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