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Simplifying 5x4 + -7x3 + -1x2 = 0 Reorder the terms: -1x2 + -7x3 + 5x4 = 0 Solving -1x2 + -7x3 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-1 + -7x + 5x2) = 0Subproblem 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 '(-1 + -7x + 5x2)' equal to zero and attempt to solve: Simplifying -1 + -7x + 5x2 = 0 Solving -1 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -1.4x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.4x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.4x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.4x + x2 = 0 + 0.2 -1.4x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1.4x + x2 = 0.2 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 0.2 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 0.2 + 0.49 Combine like terms: 0.2 + 0.49 = 0.69 0.49 + -1.4x + x2 = 0.69 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.69 Calculate the square root of the right side: 0.830662386 Break this problem into two subproblems by setting (x + -0.7) equal to 0.830662386 and -0.830662386.Subproblem 1
x + -0.7 = 0.830662386 Simplifying x + -0.7 = 0.830662386 Reorder the terms: -0.7 + x = 0.830662386 Solving -0.7 + x = 0.830662386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.830662386 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.830662386 + 0.7 x = 0.830662386 + 0.7 Combine like terms: 0.830662386 + 0.7 = 1.530662386 x = 1.530662386 Simplifying x = 1.530662386Subproblem 2
x + -0.7 = -0.830662386 Simplifying x + -0.7 = -0.830662386 Reorder the terms: -0.7 + x = -0.830662386 Solving -0.7 + x = -0.830662386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.830662386 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.830662386 + 0.7 x = -0.830662386 + 0.7 Combine like terms: -0.830662386 + 0.7 = -0.130662386 x = -0.130662386 Simplifying x = -0.130662386Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.530662386, -0.130662386}Solution
x = {0, 1.530662386, -0.130662386}
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