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Simplifying 0.20(25 + -1x) = x2 (25 * 0.20 + -1x * 0.20) = x2 (5 + -0.2x) = x2 Solving 5 + -0.2x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 5 + -0.2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 0.2x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.2x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 0.2x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.2x + x2 = 0 + 5 0.2x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.2x + x2 = 5 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 5 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 5 + 0.01 Combine like terms: 5 + 0.01 = 5.01 0.01 + 0.2x + x2 = 5.01 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 5.01 Calculate the square root of the right side: 2.238302929 Break this problem into two subproblems by setting (x + 0.1) equal to 2.238302929 and -2.238302929.Subproblem 1
x + 0.1 = 2.238302929 Simplifying x + 0.1 = 2.238302929 Reorder the terms: 0.1 + x = 2.238302929 Solving 0.1 + x = 2.238302929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 2.238302929 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 2.238302929 + -0.1 x = 2.238302929 + -0.1 Combine like terms: 2.238302929 + -0.1 = 2.138302929 x = 2.138302929 Simplifying x = 2.138302929Subproblem 2
x + 0.1 = -2.238302929 Simplifying x + 0.1 = -2.238302929 Reorder the terms: 0.1 + x = -2.238302929 Solving 0.1 + x = -2.238302929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -2.238302929 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -2.238302929 + -0.1 x = -2.238302929 + -0.1 Combine like terms: -2.238302929 + -0.1 = -2.338302929 x = -2.338302929 Simplifying x = -2.338302929Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.138302929, -2.338302929}
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