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Simplifying 1600 + -4x + -1x2 = 0 Solving 1600 + -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'. -1600 + 4x + x2 = 0 Move the constant term to the right: Add '1600' to each side of the equation. -1600 + 4x + 1600 + x2 = 0 + 1600 Reorder the terms: -1600 + 1600 + 4x + x2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + 4x + x2 = 0 + 1600 4x + x2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 4x + x2 = 1600 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 = 1600 + 4 Reorder the terms: 4 + 4x + x2 = 1600 + 4 Combine like terms: 1600 + 4 = 1604 4 + 4x + x2 = 1604 Factor a perfect square on the left side: (x + 2)(x + 2) = 1604 Calculate the square root of the right side: 40.049968789 Break this problem into two subproblems by setting (x + 2) equal to 40.049968789 and -40.049968789.Subproblem 1
x + 2 = 40.049968789 Simplifying x + 2 = 40.049968789 Reorder the terms: 2 + x = 40.049968789 Solving 2 + x = 40.049968789 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 = 40.049968789 + -2 Combine like terms: 2 + -2 = 0 0 + x = 40.049968789 + -2 x = 40.049968789 + -2 Combine like terms: 40.049968789 + -2 = 38.049968789 x = 38.049968789 Simplifying x = 38.049968789Subproblem 2
x + 2 = -40.049968789 Simplifying x + 2 = -40.049968789 Reorder the terms: 2 + x = -40.049968789 Solving 2 + x = -40.049968789 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 = -40.049968789 + -2 Combine like terms: 2 + -2 = 0 0 + x = -40.049968789 + -2 x = -40.049968789 + -2 Combine like terms: -40.049968789 + -2 = -42.049968789 x = -42.049968789 Simplifying x = -42.049968789Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.049968789, -42.049968789}
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