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Simplifying 2x2 + 5x4 + -12x3 = 0 Reorder the terms: 2x2 + -12x3 + 5x4 = 0 Solving 2x2 + -12x3 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(2 + -12x + 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 '(2 + -12x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + -12x + 5x2 = 0 Solving 2 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -2.4x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -2.4x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -2.4x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -2.4x + x2 = 0 + -0.4 -2.4x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -2.4x + x2 = -0.4 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -0.4 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -0.4 + 1.44 Combine like terms: -0.4 + 1.44 = 1.04 1.44 + -2.4x + x2 = 1.04 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (x + -1.2) equal to 1.019803903 and -1.019803903.Subproblem 1
x + -1.2 = 1.019803903 Simplifying x + -1.2 = 1.019803903 Reorder the terms: -1.2 + x = 1.019803903 Solving -1.2 + x = 1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.019803903 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.019803903 + 1.2 x = 1.019803903 + 1.2 Combine like terms: 1.019803903 + 1.2 = 2.219803903 x = 2.219803903 Simplifying x = 2.219803903Subproblem 2
x + -1.2 = -1.019803903 Simplifying x + -1.2 = -1.019803903 Reorder the terms: -1.2 + x = -1.019803903 Solving -1.2 + x = -1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.019803903 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.019803903 + 1.2 x = -1.019803903 + 1.2 Combine like terms: -1.019803903 + 1.2 = 0.180196097 x = 0.180196097 Simplifying x = 0.180196097Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.219803903, 0.180196097}Solution
x = {0, 2.219803903, 0.180196097}
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