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Simplifying -7x6 + -2x5 + 196x4 = 0 Reorder the terms: 196x4 + -2x5 + -7x6 = 0 Solving 196x4 + -2x5 + -7x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x4'. x4(196 + -2x + -7x2) = 0Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(196 + -2x + -7x2)' equal to zero and attempt to solve: Simplifying 196 + -2x + -7x2 = 0 Solving 196 + -2x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -28 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 0.2857142857x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 0.2857142857x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 0.2857142857x + x2 = 0 + 28 0.2857142857x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 0.2857142857x + x2 = 28 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 = 28 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 28 + 0.02040816328 Combine like terms: 28 + 0.02040816328 = 28.02040816328 0.02040816328 + 0.2857142857x + x2 = 28.02040816328 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 28.02040816328 Calculate the square root of the right side: 5.293430661 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 5.293430661 and -5.293430661.Subproblem 1
x + 0.1428571429 = 5.293430661 Simplifying x + 0.1428571429 = 5.293430661 Reorder the terms: 0.1428571429 + x = 5.293430661 Solving 0.1428571429 + x = 5.293430661 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 = 5.293430661 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 5.293430661 + -0.1428571429 x = 5.293430661 + -0.1428571429 Combine like terms: 5.293430661 + -0.1428571429 = 5.1505735181 x = 5.1505735181 Simplifying x = 5.1505735181Subproblem 2
x + 0.1428571429 = -5.293430661 Simplifying x + 0.1428571429 = -5.293430661 Reorder the terms: 0.1428571429 + x = -5.293430661 Solving 0.1428571429 + x = -5.293430661 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 = -5.293430661 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -5.293430661 + -0.1428571429 x = -5.293430661 + -0.1428571429 Combine like terms: -5.293430661 + -0.1428571429 = -5.4362878039 x = -5.4362878039 Simplifying x = -5.4362878039Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.1505735181, -5.4362878039}Solution
x = {5.1505735181, -5.4362878039}
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