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Simplifying 25(x + -1) + 4x = x2 Reorder the terms: 25(-1 + x) + 4x = x2 (-1 * 25 + x * 25) + 4x = x2 (-25 + 25x) + 4x = x2 Combine like terms: 25x + 4x = 29x -25 + 29x = x2 Solving -25 + 29x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 -25 + 29x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -29x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -29x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -29x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -29x + x2 = 0 + -25 -29x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -29x + x2 = -25 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -25 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -25 + 210.25 Combine like terms: -25 + 210.25 = 185.25 210.25 + -29x + x2 = 185.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 185.25 Calculate the square root of the right side: 13.610657589 Break this problem into two subproblems by setting (x + -14.5) equal to 13.610657589 and -13.610657589.Subproblem 1
x + -14.5 = 13.610657589 Simplifying x + -14.5 = 13.610657589 Reorder the terms: -14.5 + x = 13.610657589 Solving -14.5 + x = 13.610657589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 13.610657589 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 13.610657589 + 14.5 x = 13.610657589 + 14.5 Combine like terms: 13.610657589 + 14.5 = 28.110657589 x = 28.110657589 Simplifying x = 28.110657589Subproblem 2
x + -14.5 = -13.610657589 Simplifying x + -14.5 = -13.610657589 Reorder the terms: -14.5 + x = -13.610657589 Solving -14.5 + x = -13.610657589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -13.610657589 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -13.610657589 + 14.5 x = -13.610657589 + 14.5 Combine like terms: -13.610657589 + 14.5 = 0.889342411 x = 0.889342411 Simplifying x = 0.889342411Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.110657589, 0.889342411}
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