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Simplifying x2(x2 + 6x + -265) = 0 Reorder the terms: x2(-265 + 6x + x2) = 0 (-265 * x2 + 6x * x2 + x2 * x2) = 0 (-265x2 + 6x3 + x4) = 0 Solving -265x2 + 6x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-265 + 6x + x2) = 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 '(-265 + 6x + x2)' equal to zero and attempt to solve: Simplifying -265 + 6x + x2 = 0 Solving -265 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '265' to each side of the equation. -265 + 6x + 265 + x2 = 0 + 265 Reorder the terms: -265 + 265 + 6x + x2 = 0 + 265 Combine like terms: -265 + 265 = 0 0 + 6x + x2 = 0 + 265 6x + x2 = 0 + 265 Combine like terms: 0 + 265 = 265 6x + x2 = 265 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 265 + 9 Reorder the terms: 9 + 6x + x2 = 265 + 9 Combine like terms: 265 + 9 = 274 9 + 6x + x2 = 274 Factor a perfect square on the left side: (x + 3)(x + 3) = 274 Calculate the square root of the right side: 16.552945357 Break this problem into two subproblems by setting (x + 3) equal to 16.552945357 and -16.552945357.Subproblem 1
x + 3 = 16.552945357 Simplifying x + 3 = 16.552945357 Reorder the terms: 3 + x = 16.552945357 Solving 3 + x = 16.552945357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 16.552945357 + -3 Combine like terms: 3 + -3 = 0 0 + x = 16.552945357 + -3 x = 16.552945357 + -3 Combine like terms: 16.552945357 + -3 = 13.552945357 x = 13.552945357 Simplifying x = 13.552945357Subproblem 2
x + 3 = -16.552945357 Simplifying x + 3 = -16.552945357 Reorder the terms: 3 + x = -16.552945357 Solving 3 + x = -16.552945357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -16.552945357 + -3 Combine like terms: 3 + -3 = 0 0 + x = -16.552945357 + -3 x = -16.552945357 + -3 Combine like terms: -16.552945357 + -3 = -19.552945357 x = -19.552945357 Simplifying x = -19.552945357Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.552945357, -19.552945357}Solution
x = {0, 13.552945357, -19.552945357}
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