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Simplifying 0.02(25 + -1x) = x2 (25 * 0.02 + -1x * 0.02) = x2 (0.5 + -0.02x) = x2 Solving 0.5 + -0.02x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.5 + -0.02x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.5 + 0.02x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.02x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.02x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.02x + x2 = 0 + 0.5 0.02x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.02x + x2 = 0.5 The x term is 0.02x. Take half its coefficient (0.01). Square it (0.0001) and add it to both sides. Add '0.0001' to each side of the equation. 0.02x + 0.0001 + x2 = 0.5 + 0.0001 Reorder the terms: 0.0001 + 0.02x + x2 = 0.5 + 0.0001 Combine like terms: 0.5 + 0.0001 = 0.5001 0.0001 + 0.02x + x2 = 0.5001 Factor a perfect square on the left side: (x + 0.01)(x + 0.01) = 0.5001 Calculate the square root of the right side: 0.707177488 Break this problem into two subproblems by setting (x + 0.01) equal to 0.707177488 and -0.707177488.Subproblem 1
x + 0.01 = 0.707177488 Simplifying x + 0.01 = 0.707177488 Reorder the terms: 0.01 + x = 0.707177488 Solving 0.01 + x = 0.707177488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01' to each side of the equation. 0.01 + -0.01 + x = 0.707177488 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = 0.707177488 + -0.01 x = 0.707177488 + -0.01 Combine like terms: 0.707177488 + -0.01 = 0.697177488 x = 0.697177488 Simplifying x = 0.697177488Subproblem 2
x + 0.01 = -0.707177488 Simplifying x + 0.01 = -0.707177488 Reorder the terms: 0.01 + x = -0.707177488 Solving 0.01 + x = -0.707177488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01' to each side of the equation. 0.01 + -0.01 + x = -0.707177488 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = -0.707177488 + -0.01 x = -0.707177488 + -0.01 Combine like terms: -0.707177488 + -0.01 = -0.717177488 x = -0.717177488 Simplifying x = -0.717177488Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.697177488, -0.717177488}
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