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Simplifying x(2x + -4) = 665 Reorder the terms: x(-4 + 2x) = 665 (-4 * x + 2x * x) = 665 (-4x + 2x2) = 665 Solving -4x + 2x2 = 665 Solving for variable 'x'. Reorder the terms: -665 + -4x + 2x2 = 665 + -665 Combine like terms: 665 + -665 = 0 -665 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -332.5 + -2x + x2 = 0 Move the constant term to the right: Add '332.5' to each side of the equation. -332.5 + -2x + 332.5 + x2 = 0 + 332.5 Reorder the terms: -332.5 + 332.5 + -2x + x2 = 0 + 332.5 Combine like terms: -332.5 + 332.5 = 0.0 0.0 + -2x + x2 = 0 + 332.5 -2x + x2 = 0 + 332.5 Combine like terms: 0 + 332.5 = 332.5 -2x + x2 = 332.5 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 = 332.5 + 1 Reorder the terms: 1 + -2x + x2 = 332.5 + 1 Combine like terms: 332.5 + 1 = 333.5 1 + -2x + x2 = 333.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 333.5 Calculate the square root of the right side: 18.261982368 Break this problem into two subproblems by setting (x + -1) equal to 18.261982368 and -18.261982368.Subproblem 1
x + -1 = 18.261982368 Simplifying x + -1 = 18.261982368 Reorder the terms: -1 + x = 18.261982368 Solving -1 + x = 18.261982368 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 = 18.261982368 + 1 Combine like terms: -1 + 1 = 0 0 + x = 18.261982368 + 1 x = 18.261982368 + 1 Combine like terms: 18.261982368 + 1 = 19.261982368 x = 19.261982368 Simplifying x = 19.261982368Subproblem 2
x + -1 = -18.261982368 Simplifying x + -1 = -18.261982368 Reorder the terms: -1 + x = -18.261982368 Solving -1 + x = -18.261982368 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 = -18.261982368 + 1 Combine like terms: -1 + 1 = 0 0 + x = -18.261982368 + 1 x = -18.261982368 + 1 Combine like terms: -18.261982368 + 1 = -17.261982368 x = -17.261982368 Simplifying x = -17.261982368Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.261982368, -17.261982368}
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