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Simplifying 0 = 7x2 + 14x + 3 Reorder the terms: 0 = 3 + 14x + 7x2 Solving 0 = 3 + 14x + 7x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -14x + -7x2 = 3 + 14x + 7x2 + -3 + -14x + -7x2 Reorder the terms: -3 + -14x + -7x2 = 3 + -3 + 14x + -14x + 7x2 + -7x2 Combine like terms: 3 + -3 = 0 -3 + -14x + -7x2 = 0 + 14x + -14x + 7x2 + -7x2 -3 + -14x + -7x2 = 14x + -14x + 7x2 + -7x2 Combine like terms: 14x + -14x = 0 -3 + -14x + -7x2 = 0 + 7x2 + -7x2 -3 + -14x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -3 + -14x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 14x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 14x + 7x2)' equal to zero and attempt to solve: Simplifying 3 + 14x + 7x2 = 0 Solving 3 + 14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + 2x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + 2x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + 2x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.4285714286 2x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 2x + x2 = -0.4285714286 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.4285714286 + 1 Reorder the terms: 1 + 2x + x2 = -0.4285714286 + 1 Combine like terms: -0.4285714286 + 1 = 0.5714285714 1 + 2x + x2 = 0.5714285714 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.5714285714 Calculate the square root of the right side: 0.755928946 Break this problem into two subproblems by setting (x + 1) equal to 0.755928946 and -0.755928946.Subproblem 1
x + 1 = 0.755928946 Simplifying x + 1 = 0.755928946 Reorder the terms: 1 + x = 0.755928946 Solving 1 + x = 0.755928946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.755928946 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.755928946 + -1 x = 0.755928946 + -1 Combine like terms: 0.755928946 + -1 = -0.244071054 x = -0.244071054 Simplifying x = -0.244071054Subproblem 2
x + 1 = -0.755928946 Simplifying x + 1 = -0.755928946 Reorder the terms: 1 + x = -0.755928946 Solving 1 + x = -0.755928946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.755928946 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.755928946 + -1 x = -0.755928946 + -1 Combine like terms: -0.755928946 + -1 = -1.755928946 x = -1.755928946 Simplifying x = -1.755928946Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.244071054, -1.755928946}Solution
x = {-0.244071054, -1.755928946}
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