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Simplifying (5x + -1) * x = 25 Reorder the terms: (-1 + 5x) * x = 25 Reorder the terms for easier multiplication: x(-1 + 5x) = 25 (-1 * x + 5x * x) = 25 (-1x + 5x2) = 25 Solving -1x + 5x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -1x + 5x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -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 = 2.338302929 x = 2.338302929 Simplifying x = 2.338302929Subproblem 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 = -2.138302929 x = -2.138302929 Simplifying x = -2.138302929Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.338302929, -2.138302929}
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