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Simplifying 4x + -5x3 + 6x2 = 0 Reorder the terms: 4x + 6x2 + -5x3 = 0 Solving 4x + 6x2 + -5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(4 + 6x + -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 '(4 + 6x + -5x2)' equal to zero and attempt to solve: Simplifying 4 + 6x + -5x2 = 0 Solving 4 + 6x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.8 + -1.2x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1.2x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1.2x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1.2x + x2 = 0 + 0.8 -1.2x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -1.2x + x2 = 0.8 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 0.8 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.8 + 0.36 Combine like terms: 0.8 + 0.36 = 1.16 0.36 + -1.2x + x2 = 1.16 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 1.16 Calculate the square root of the right side: 1.077032961 Break this problem into two subproblems by setting (x + -0.6) equal to 1.077032961 and -1.077032961.Subproblem 1
x + -0.6 = 1.077032961 Simplifying x + -0.6 = 1.077032961 Reorder the terms: -0.6 + x = 1.077032961 Solving -0.6 + x = 1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.077032961 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.077032961 + 0.6 x = 1.077032961 + 0.6 Combine like terms: 1.077032961 + 0.6 = 1.677032961 x = 1.677032961 Simplifying x = 1.677032961Subproblem 2
x + -0.6 = -1.077032961 Simplifying x + -0.6 = -1.077032961 Reorder the terms: -0.6 + x = -1.077032961 Solving -0.6 + x = -1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.077032961 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.077032961 + 0.6 x = -1.077032961 + 0.6 Combine like terms: -1.077032961 + 0.6 = -0.477032961 x = -0.477032961 Simplifying x = -0.477032961Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.677032961, -0.477032961}Solution
x = {0, 1.677032961, -0.477032961}
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