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Simplifying 3x4 = 10x2 + -6x3 Solving 3x4 = 10x2 + -6x3 Solving for variable 'x'. Reorder the terms: -10x2 + 6x3 + 3x4 = 10x2 + -6x3 + -10x2 + 6x3 Reorder the terms: -10x2 + 6x3 + 3x4 = 10x2 + -10x2 + -6x3 + 6x3 Combine like terms: 10x2 + -10x2 = 0 -10x2 + 6x3 + 3x4 = 0 + -6x3 + 6x3 -10x2 + 6x3 + 3x4 = -6x3 + 6x3 Combine like terms: -6x3 + 6x3 = 0 -10x2 + 6x3 + 3x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-10 + 6x + 3x2) = 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 '(-10 + 6x + 3x2)' equal to zero and attempt to solve: Simplifying -10 + 6x + 3x2 = 0 Solving -10 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + 2x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 2x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 2x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 2x + x2 = 0 + 3.333333333 2x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 2x + x2 = 3.333333333 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 = 3.333333333 + 1 Reorder the terms: 1 + 2x + x2 = 3.333333333 + 1 Combine like terms: 3.333333333 + 1 = 4.333333333 1 + 2x + x2 = 4.333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 4.333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (x + 1) equal to 2.081665999 and -2.081665999.Subproblem 1
x + 1 = 2.081665999 Simplifying x + 1 = 2.081665999 Reorder the terms: 1 + x = 2.081665999 Solving 1 + x = 2.081665999 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 = 2.081665999 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.081665999 + -1 x = 2.081665999 + -1 Combine like terms: 2.081665999 + -1 = 1.081665999 x = 1.081665999 Simplifying x = 1.081665999Subproblem 2
x + 1 = -2.081665999 Simplifying x + 1 = -2.081665999 Reorder the terms: 1 + x = -2.081665999 Solving 1 + x = -2.081665999 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 = -2.081665999 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.081665999 + -1 x = -2.081665999 + -1 Combine like terms: -2.081665999 + -1 = -3.081665999 x = -3.081665999 Simplifying x = -3.081665999Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.081665999, -3.081665999}Solution
x = {0, 1.081665999, -3.081665999}
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