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Simplifying x(2x + -4) = 35 Reorder the terms: x(-4 + 2x) = 35 (-4 * x + 2x * x) = 35 (-4x + 2x2) = 35 Solving -4x + 2x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + -4x + 2x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -2x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -2x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -2x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -2x + x2 = 0 + 17.5 -2x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -2x + x2 = 17.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 17.5 + 1 Reorder the terms: 1 + -2x + x2 = 17.5 + 1 Combine like terms: 17.5 + 1 = 18.5 1 + -2x + x2 = 18.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (x + -1) equal to 4.301162634 and -4.301162634.Subproblem 1
x + -1 = 4.301162634 Simplifying x + -1 = 4.301162634 Reorder the terms: -1 + x = 4.301162634 Solving -1 + x = 4.301162634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.301162634 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.301162634 + 1 x = 4.301162634 + 1 Combine like terms: 4.301162634 + 1 = 5.301162634 x = 5.301162634 Simplifying x = 5.301162634Subproblem 2
x + -1 = -4.301162634 Simplifying x + -1 = -4.301162634 Reorder the terms: -1 + x = -4.301162634 Solving -1 + x = -4.301162634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.301162634 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.301162634 + 1 x = -4.301162634 + 1 Combine like terms: -4.301162634 + 1 = -3.301162634 x = -3.301162634 Simplifying x = -3.301162634Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.301162634, -3.301162634}
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