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Simplifying x(x2 + -10x + 13) = 0 Reorder the terms: x(13 + -10x + x2) = 0 (13 * x + -10x * x + x2 * x) = 0 (13x + -10x2 + x3) = 0 Solving 13x + -10x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(13 + -10x + x2) = 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 '(13 + -10x + x2)' equal to zero and attempt to solve: Simplifying 13 + -10x + x2 = 0 Solving 13 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -10x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -10x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -10x + x2 = 0 + -13 -10x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -10x + x2 = -13 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -13 + 25 Reorder the terms: 25 + -10x + x2 = -13 + 25 Combine like terms: -13 + 25 = 12 25 + -10x + x2 = 12 Factor a perfect square on the left side: (x + -5)(x + -5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -5) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -5 = 3.464101615 Simplifying x + -5 = 3.464101615 Reorder the terms: -5 + x = 3.464101615 Solving -5 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.464101615 + 5 x = 3.464101615 + 5 Combine like terms: 3.464101615 + 5 = 8.464101615 x = 8.464101615 Simplifying x = 8.464101615Subproblem 2
x + -5 = -3.464101615 Simplifying x + -5 = -3.464101615 Reorder the terms: -5 + x = -3.464101615 Solving -5 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.464101615 + 5 x = -3.464101615 + 5 Combine like terms: -3.464101615 + 5 = 1.535898385 x = 1.535898385 Simplifying x = 1.535898385Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.464101615, 1.535898385}Solution
x = {0, 8.464101615, 1.535898385}
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