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Simplifying 3x2 + 8x + -5x3 + 7x2 + -2x = 0 Reorder the terms: 8x + -2x + 3x2 + 7x2 + -5x3 = 0 Combine like terms: 8x + -2x = 6x 6x + 3x2 + 7x2 + -5x3 = 0 Combine like terms: 3x2 + 7x2 = 10x2 6x + 10x2 + -5x3 = 0 Solving 6x + 10x2 + -5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(6 + 10x + -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 '(6 + 10x + -5x2)' equal to zero and attempt to solve: Simplifying 6 + 10x + -5x2 = 0 Solving 6 + 10x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.2 + -2x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -2x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -2x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -2x + x2 = 0 + 1.2 -2x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -2x + x2 = 1.2 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.2 + 1 Reorder the terms: 1 + -2x + x2 = 1.2 + 1 Combine like terms: 1.2 + 1 = 2.2 1 + -2x + x2 = 2.2 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.2 Calculate the square root of the right side: 1.483239697 Break this problem into two subproblems by setting (x + -1) equal to 1.483239697 and -1.483239697.Subproblem 1
x + -1 = 1.483239697 Simplifying x + -1 = 1.483239697 Reorder the terms: -1 + x = 1.483239697 Solving -1 + x = 1.483239697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.483239697 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.483239697 + 1 x = 1.483239697 + 1 Combine like terms: 1.483239697 + 1 = 2.483239697 x = 2.483239697 Simplifying x = 2.483239697Subproblem 2
x + -1 = -1.483239697 Simplifying x + -1 = -1.483239697 Reorder the terms: -1 + x = -1.483239697 Solving -1 + x = -1.483239697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.483239697 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.483239697 + 1 x = -1.483239697 + 1 Combine like terms: -1.483239697 + 1 = -0.483239697 x = -0.483239697 Simplifying x = -0.483239697Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.483239697, -0.483239697}Solution
x = {0, 2.483239697, -0.483239697}
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