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Simplifying 14x2 + 4x + -8 = 0 Reorder the terms: -8 + 4x + 14x2 = 0 Solving -8 + 4x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 2x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 2x + 7x2)' equal to zero and attempt to solve: Simplifying -4 + 2x + 7x2 = 0 Solving -4 + 2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 0.2857142857x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 0.2857142857x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 0.2857142857x + x2 = 0 + 0.5714285714 0.2857142857x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 0.2857142857x + x2 = 0.5714285714 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = 0.5714285714 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 0.5714285714 + 0.02040816328 Combine like terms: 0.5714285714 + 0.02040816328 = 0.59183673468 0.02040816328 + 0.2857142857x + x2 = 0.59183673468 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 0.59183673468 Calculate the square root of the right side: 0.769309258 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 0.769309258 and -0.769309258.Subproblem 1
x + 0.1428571429 = 0.769309258 Simplifying x + 0.1428571429 = 0.769309258 Reorder the terms: 0.1428571429 + x = 0.769309258 Solving 0.1428571429 + x = 0.769309258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = 0.769309258 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 0.769309258 + -0.1428571429 x = 0.769309258 + -0.1428571429 Combine like terms: 0.769309258 + -0.1428571429 = 0.6264521151 x = 0.6264521151 Simplifying x = 0.6264521151Subproblem 2
x + 0.1428571429 = -0.769309258 Simplifying x + 0.1428571429 = -0.769309258 Reorder the terms: 0.1428571429 + x = -0.769309258 Solving 0.1428571429 + x = -0.769309258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = -0.769309258 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -0.769309258 + -0.1428571429 x = -0.769309258 + -0.1428571429 Combine like terms: -0.769309258 + -0.1428571429 = -0.9121664009 x = -0.9121664009 Simplifying x = -0.9121664009Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6264521151, -0.9121664009}Solution
x = {0.6264521151, -0.9121664009}
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