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Simplifying 7x(2x + -4) + 6 = 0 Reorder the terms: 7x(-4 + 2x) + 6 = 0 (-4 * 7x + 2x * 7x) + 6 = 0 (-28x + 14x2) + 6 = 0 Reorder the terms: 6 + -28x + 14x2 = 0 Solving 6 + -28x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -14x + 7x2) = 0 Ignore the factor 2.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 = 1.755928946 x = 1.755928946 Simplifying x = 1.755928946Subproblem 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 = 0.244071054 x = 0.244071054 Simplifying x = 0.244071054Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.755928946, 0.244071054}Solution
x = {1.755928946, 0.244071054}
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