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Simplifying x(8 + -1x) + 2x = 1 (8 * x + -1x * x) + 2x = 1 (8x + -1x2) + 2x = 1 Reorder the terms: 8x + 2x + -1x2 = 1 Combine like terms: 8x + 2x = 10x 10x + -1x2 = 1 Solving 10x + -1x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 10x + -1x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -10x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -10x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -10x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10x + x2 = 0 + -1 -10x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -10x + x2 = -1 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 = -1 + 25 Reorder the terms: 25 + -10x + x2 = -1 + 25 Combine like terms: -1 + 25 = 24 25 + -10x + x2 = 24 Factor a perfect square on the left side: (x + -5)(x + -5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -5) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -5 = 4.898979486 Simplifying x + -5 = 4.898979486 Reorder the terms: -5 + x = 4.898979486 Solving -5 + x = 4.898979486 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 = 4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.898979486 + 5 x = 4.898979486 + 5 Combine like terms: 4.898979486 + 5 = 9.898979486 x = 9.898979486 Simplifying x = 9.898979486Subproblem 2
x + -5 = -4.898979486 Simplifying x + -5 = -4.898979486 Reorder the terms: -5 + x = -4.898979486 Solving -5 + x = -4.898979486 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 = -4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.898979486 + 5 x = -4.898979486 + 5 Combine like terms: -4.898979486 + 5 = 0.101020514 x = 0.101020514 Simplifying x = 0.101020514Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.898979486, 0.101020514}
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