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Simplifying -1x * x + -4x + 640 = 0 Multiply x * x -1x2 + -4x + 640 = 0 Reorder the terms: 640 + -4x + -1x2 = 0 Solving 640 + -4x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -640 + 4x + x2 = 0 Move the constant term to the right: Add '640' to each side of the equation. -640 + 4x + 640 + x2 = 0 + 640 Reorder the terms: -640 + 640 + 4x + x2 = 0 + 640 Combine like terms: -640 + 640 = 0 0 + 4x + x2 = 0 + 640 4x + x2 = 0 + 640 Combine like terms: 0 + 640 = 640 4x + x2 = 640 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 640 + 4 Reorder the terms: 4 + 4x + x2 = 640 + 4 Combine like terms: 640 + 4 = 644 4 + 4x + x2 = 644 Factor a perfect square on the left side: (x + 2)(x + 2) = 644 Calculate the square root of the right side: 25.377155081 Break this problem into two subproblems by setting (x + 2) equal to 25.377155081 and -25.377155081.Subproblem 1
x + 2 = 25.377155081 Simplifying x + 2 = 25.377155081 Reorder the terms: 2 + x = 25.377155081 Solving 2 + x = 25.377155081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 25.377155081 + -2 Combine like terms: 2 + -2 = 0 0 + x = 25.377155081 + -2 x = 25.377155081 + -2 Combine like terms: 25.377155081 + -2 = 23.377155081 x = 23.377155081 Simplifying x = 23.377155081Subproblem 2
x + 2 = -25.377155081 Simplifying x + 2 = -25.377155081 Reorder the terms: 2 + x = -25.377155081 Solving 2 + x = -25.377155081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -25.377155081 + -2 Combine like terms: 2 + -2 = 0 0 + x = -25.377155081 + -2 x = -25.377155081 + -2 Combine like terms: -25.377155081 + -2 = -27.377155081 x = -27.377155081 Simplifying x = -27.377155081Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.377155081, -27.377155081}
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