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Simplifying 7x(x + -1) = 25 Reorder the terms: 7x(-1 + x) = 25 (-1 * 7x + x * 7x) = 25 (-7x + 7x2) = 25 Solving -7x + 7x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -7x + 7x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -7x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.571428571 + -1x + x2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + -1x + 3.571428571 + x2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + -1x + x2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + -1x + x2 = 0 + 3.571428571 -1x + x2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 -1x + x2 = 3.571428571 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 3.571428571 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3.571428571 + 0.25 Combine like terms: 3.571428571 + 0.25 = 3.821428571 0.25 + -1x + x2 = 3.821428571 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.821428571 Calculate the square root of the right side: 1.954847455 Break this problem into two subproblems by setting (x + -0.5) equal to 1.954847455 and -1.954847455.Subproblem 1
x + -0.5 = 1.954847455 Simplifying x + -0.5 = 1.954847455 Reorder the terms: -0.5 + x = 1.954847455 Solving -0.5 + x = 1.954847455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.954847455 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.954847455 + 0.5 x = 1.954847455 + 0.5 Combine like terms: 1.954847455 + 0.5 = 2.454847455 x = 2.454847455 Simplifying x = 2.454847455Subproblem 2
x + -0.5 = -1.954847455 Simplifying x + -0.5 = -1.954847455 Reorder the terms: -0.5 + x = -1.954847455 Solving -0.5 + x = -1.954847455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.954847455 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.954847455 + 0.5 x = -1.954847455 + 0.5 Combine like terms: -1.954847455 + 0.5 = -1.454847455 x = -1.454847455 Simplifying x = -1.454847455Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.454847455, -1.454847455}
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