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Simplifying 25x2 + 0.01 = x Reorder the terms: 0.01 + 25x2 = x Solving 0.01 + 25x2 = x Solving for variable 'x'. Reorder the terms: 0.01 + -1x + 25x2 = x + -1x Combine like terms: x + -1x = 0 0.01 + -1x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.0004 + -0.04x + x2 = 0 Move the constant term to the right: Add '-0.0004' to each side of the equation. 0.0004 + -0.04x + -0.0004 + x2 = 0 + -0.0004 Reorder the terms: 0.0004 + -0.0004 + -0.04x + x2 = 0 + -0.0004 Combine like terms: 0.0004 + -0.0004 = 0.0000 0.0000 + -0.04x + x2 = 0 + -0.0004 -0.04x + x2 = 0 + -0.0004 Combine like terms: 0 + -0.0004 = -0.0004 -0.04x + x2 = -0.0004 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 = -0.0004 + 0.0004 Reorder the terms: 0.0004 + -0.04x + x2 = -0.0004 + 0.0004 Combine like terms: -0.0004 + 0.0004 = 0.0000 0.0004 + -0.04x + x2 = 0.0000 Factor a perfect square on the left side: (x + -0.02)(x + -0.02) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + -0.02) equal to 0.0000 and 0.0000.Subproblem 1
x + -0.02 = 0.0000 Simplifying x + -0.02 = 0.0000 Reorder the terms: -0.02 + x = 0.0000 Solving -0.02 + x = 0.0000 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 = 0.0000 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = 0.0000 + 0.02 x = 0.0000 + 0.02 Combine like terms: 0.0000 + 0.02 = 0.02 x = 0.02 Simplifying x = 0.02Subproblem 2
x + -0.02 = 0.0000 Simplifying x + -0.02 = 0.0000 Reorder the terms: -0.02 + x = 0.0000 Solving -0.02 + x = 0.0000 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 = 0.0000 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = 0.0000 + 0.02 x = 0.0000 + 0.02 Combine like terms: 0.0000 + 0.02 = 0.02 x = 0.02 Simplifying x = 0.02Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.02, 0.02}
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