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Simplifying 2x(x + -5) = 35 Reorder the terms: 2x(-5 + x) = 35 (-5 * 2x + x * 2x) = 35 (-10x + 2x2) = 35 Solving -10x + 2x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + -10x + 2x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -5x + x2 = 0 + 17.5 -5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -5x + x2 = 17.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 17.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 17.5 + 6.25 Combine like terms: 17.5 + 6.25 = 23.75 6.25 + -5x + x2 = 23.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 23.75 Calculate the square root of the right side: 4.873397172 Break this problem into two subproblems by setting (x + -2.5) equal to 4.873397172 and -4.873397172.Subproblem 1
x + -2.5 = 4.873397172 Simplifying x + -2.5 = 4.873397172 Reorder the terms: -2.5 + x = 4.873397172 Solving -2.5 + x = 4.873397172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.873397172 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.873397172 + 2.5 x = 4.873397172 + 2.5 Combine like terms: 4.873397172 + 2.5 = 7.373397172 x = 7.373397172 Simplifying x = 7.373397172Subproblem 2
x + -2.5 = -4.873397172 Simplifying x + -2.5 = -4.873397172 Reorder the terms: -2.5 + x = -4.873397172 Solving -2.5 + x = -4.873397172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.873397172 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.873397172 + 2.5 x = -4.873397172 + 2.5 Combine like terms: -4.873397172 + 2.5 = -2.373397172 x = -2.373397172 Simplifying x = -2.373397172Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.373397172, -2.373397172}
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