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Simplifying 16x2 + 96x + 112 = 0 Reorder the terms: 112 + 96x + 16x2 = 0 Solving 112 + 96x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(7 + 6x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(7 + 6x + x2)' equal to zero and attempt to solve: Simplifying 7 + 6x + x2 = 0 Solving 7 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 6x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6x + x2 = 0 + -7 6x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 6x + x2 = -7 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -7 + 9 Reorder the terms: 9 + 6x + x2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + 6x + x2 = 2 Factor a perfect square on the left side: (x + 3)(x + 3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 3) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 3 = 1.414213562 Simplifying x + 3 = 1.414213562 Reorder the terms: 3 + x = 1.414213562 Solving 3 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.414213562 + -3 x = 1.414213562 + -3 Combine like terms: 1.414213562 + -3 = -1.585786438 x = -1.585786438 Simplifying x = -1.585786438Subproblem 2
x + 3 = -1.414213562 Simplifying x + 3 = -1.414213562 Reorder the terms: 3 + x = -1.414213562 Solving 3 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.414213562 + -3 x = -1.414213562 + -3 Combine like terms: -1.414213562 + -3 = -4.414213562 x = -4.414213562 Simplifying x = -4.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.585786438, -4.414213562}Solution
x = {-1.585786438, -4.414213562}
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