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Simplifying 2x2(x + 1) = 6x Reorder the terms: 2x2(1 + x) = 6x (1 * 2x2 + x * 2x2) = 6x (2x2 + 2x3) = 6x Solving 2x2 + 2x3 = 6x Solving for variable 'x'. Reorder the terms: -6x + 2x2 + 2x3 = 6x + -6x Combine like terms: 6x + -6x = 0 -6x + 2x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-3 + x + x2) = 0 Ignore the factor 2.Subproblem 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 '(-3 + x + x2)' equal to zero and attempt to solve: Simplifying -3 + x + x2 = 0 Solving -3 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x + x2 = 0 + 3 x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 x + x2 = 3 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 3 + 0.25 Reorder the terms: 0.25 + x + x2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + x + x2 = 3.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 0.5 = 1.802775638 Simplifying x + 0.5 = 1.802775638 Reorder the terms: 0.5 + x = 1.802775638 Solving 0.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.802775638 + -0.5 x = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 x = 1.302775638 Simplifying x = 1.302775638Subproblem 2
x + 0.5 = -1.802775638 Simplifying x + 0.5 = -1.802775638 Reorder the terms: 0.5 + x = -1.802775638 Solving 0.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.802775638 + -0.5 x = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 x = -2.302775638 Simplifying x = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.302775638, -2.302775638}Solution
x = {0, 1.302775638, -2.302775638}
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