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Simplifying 25x2 + -1x + -50 = 0 Reorder the terms: -50 + -1x + 25x2 = 0 Solving -50 + -1x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2 + -0.04x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.04x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.04x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.04x + x2 = 0 + 2 -0.04x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.04x + x2 = 2 The x term is -0.04x. Take half its coefficient (-0.02). Square it (0.0004) and add it to both sides. Add '0.0004' to each side of the equation. -0.04x + 0.0004 + x2 = 2 + 0.0004 Reorder the terms: 0.0004 + -0.04x + x2 = 2 + 0.0004 Combine like terms: 2 + 0.0004 = 2.0004 0.0004 + -0.04x + x2 = 2.0004 Factor a perfect square on the left side: (x + -0.02)(x + -0.02) = 2.0004 Calculate the square root of the right side: 1.414354977 Break this problem into two subproblems by setting (x + -0.02) equal to 1.414354977 and -1.414354977.Subproblem 1
x + -0.02 = 1.414354977 Simplifying x + -0.02 = 1.414354977 Reorder the terms: -0.02 + x = 1.414354977 Solving -0.02 + x = 1.414354977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = 1.414354977 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = 1.414354977 + 0.02 x = 1.414354977 + 0.02 Combine like terms: 1.414354977 + 0.02 = 1.434354977 x = 1.434354977 Simplifying x = 1.434354977Subproblem 2
x + -0.02 = -1.414354977 Simplifying x + -0.02 = -1.414354977 Reorder the terms: -0.02 + x = -1.414354977 Solving -0.02 + x = -1.414354977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = -1.414354977 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = -1.414354977 + 0.02 x = -1.414354977 + 0.02 Combine like terms: -1.414354977 + 0.02 = -1.394354977 x = -1.394354977 Simplifying x = -1.394354977Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.434354977, -1.394354977}
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