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Simplifying 5x3 + -7x2 + -25x = 0 Reorder the terms: -25x + -7x2 + 5x3 = 0 Solving -25x + -7x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-25 + -7x + 5x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-25 + -7x + 5x2)' equal to zero and attempt to solve: Simplifying -25 + -7x + 5x2 = 0 Solving -25 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5 + -1.4x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1.4x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -1.4x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1.4x + x2 = 0 + 5 -1.4x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1.4x + x2 = 5 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 = 5 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 5 + 0.49 Combine like terms: 5 + 0.49 = 5.49 0.49 + -1.4x + x2 = 5.49 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 5.49 Calculate the square root of the right side: 2.343074903 Break this problem into two subproblems by setting (x + -0.7) equal to 2.343074903 and -2.343074903.Subproblem 1
x + -0.7 = 2.343074903 Simplifying x + -0.7 = 2.343074903 Reorder the terms: -0.7 + x = 2.343074903 Solving -0.7 + x = 2.343074903 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 = 2.343074903 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 2.343074903 + 0.7 x = 2.343074903 + 0.7 Combine like terms: 2.343074903 + 0.7 = 3.043074903 x = 3.043074903 Simplifying x = 3.043074903Subproblem 2
x + -0.7 = -2.343074903 Simplifying x + -0.7 = -2.343074903 Reorder the terms: -0.7 + x = -2.343074903 Solving -0.7 + x = -2.343074903 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 = -2.343074903 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -2.343074903 + 0.7 x = -2.343074903 + 0.7 Combine like terms: -2.343074903 + 0.7 = -1.643074903 x = -1.643074903 Simplifying x = -1.643074903Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.043074903, -1.643074903}Solution
x = {0, 3.043074903, -1.643074903}
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