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Simplifying 49x4 + -14x3 + -28x2 = 0 Reorder the terms: -28x2 + -14x3 + 49x4 = 0 Solving -28x2 + -14x3 + 49x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7x2'. 7x2(-4 + -2x + 7x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
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 = 0.9121664009 x = 0.9121664009 Simplifying x = 0.9121664009Subproblem 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 = -0.6264521151 x = -0.6264521151 Simplifying x = -0.6264521151Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9121664009, -0.6264521151}Solution
x = {0, 0.9121664009, -0.6264521151}
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