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Simplifying x(-1) = x2(-1) + -10x(-1) + -3 Reorder the terms for easier multiplication: -1x = x2(-1) + -10x(-1) + -3 Reorder the terms for easier multiplication: -1x = -1x2 + -10x(-1) + -3 Reorder the terms for easier multiplication: -1x = -1x2 + -10 * -1x + -3 Multiply -10 * -1 -1x = -1x2 + 10x + -3 Reorder the terms: -1x = -3 + 10x + -1x2 Solving -1x = -3 + 10x + -1x2 Solving for variable 'x'. Reorder the terms: 3 + -1x + -10x + x2 = -3 + 10x + -1x2 + 3 + -10x + x2 Combine like terms: -1x + -10x = -11x 3 + -11x + x2 = -3 + 10x + -1x2 + 3 + -10x + x2 Reorder the terms: 3 + -11x + x2 = -3 + 3 + 10x + -10x + -1x2 + x2 Combine like terms: -3 + 3 = 0 3 + -11x + x2 = 0 + 10x + -10x + -1x2 + x2 3 + -11x + x2 = 10x + -10x + -1x2 + x2 Combine like terms: 10x + -10x = 0 3 + -11x + x2 = 0 + -1x2 + x2 3 + -11x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 3 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -11x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -11x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -11x + x2 = 0 + -3 -11x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -11x + x2 = -3 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -3 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -3 + 30.25 Combine like terms: -3 + 30.25 = 27.25 30.25 + -11x + x2 = 27.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + -5.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + -5.5 = 5.220153254 Simplifying x + -5.5 = 5.220153254 Reorder the terms: -5.5 + x = 5.220153254 Solving -5.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.220153254 + 5.5 x = 5.220153254 + 5.5 Combine like terms: 5.220153254 + 5.5 = 10.720153254 x = 10.720153254 Simplifying x = 10.720153254Subproblem 2
x + -5.5 = -5.220153254 Simplifying x + -5.5 = -5.220153254 Reorder the terms: -5.5 + x = -5.220153254 Solving -5.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.220153254 + 5.5 x = -5.220153254 + 5.5 Combine like terms: -5.220153254 + 5.5 = 0.279846746 x = 0.279846746 Simplifying x = 0.279846746Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.720153254, 0.279846746}
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