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Simplifying 5x(x + -5) = x(4x + 6) + -52 Reorder the terms: 5x(-5 + x) = x(4x + 6) + -52 (-5 * 5x + x * 5x) = x(4x + 6) + -52 (-25x + 5x2) = x(4x + 6) + -52 Reorder the terms: -25x + 5x2 = x(6 + 4x) + -52 -25x + 5x2 = (6 * x + 4x * x) + -52 -25x + 5x2 = (6x + 4x2) + -52 Reorder the terms: -25x + 5x2 = -52 + 6x + 4x2 Solving -25x + 5x2 = -52 + 6x + 4x2 Solving for variable 'x'. Reorder the terms: 52 + -25x + -6x + 5x2 + -4x2 = -52 + 6x + 4x2 + 52 + -6x + -4x2 Combine like terms: -25x + -6x = -31x 52 + -31x + 5x2 + -4x2 = -52 + 6x + 4x2 + 52 + -6x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 52 + -31x + 1x2 = -52 + 6x + 4x2 + 52 + -6x + -4x2 Reorder the terms: 52 + -31x + 1x2 = -52 + 52 + 6x + -6x + 4x2 + -4x2 Combine like terms: -52 + 52 = 0 52 + -31x + 1x2 = 0 + 6x + -6x + 4x2 + -4x2 52 + -31x + 1x2 = 6x + -6x + 4x2 + -4x2 Combine like terms: 6x + -6x = 0 52 + -31x + 1x2 = 0 + 4x2 + -4x2 52 + -31x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 52 + -31x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + -31x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + -31x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -31x + x2 = 0 + -52 -31x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 -31x + x2 = -52 The x term is -31x. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31x + 240.25 + x2 = -52 + 240.25 Reorder the terms: 240.25 + -31x + x2 = -52 + 240.25 Combine like terms: -52 + 240.25 = 188.25 240.25 + -31x + x2 = 188.25 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 188.25 Calculate the square root of the right side: 13.720422734 Break this problem into two subproblems by setting (x + -15.5) equal to 13.720422734 and -13.720422734.Subproblem 1
x + -15.5 = 13.720422734 Simplifying x + -15.5 = 13.720422734 Reorder the terms: -15.5 + x = 13.720422734 Solving -15.5 + x = 13.720422734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = 13.720422734 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 13.720422734 + 15.5 x = 13.720422734 + 15.5 Combine like terms: 13.720422734 + 15.5 = 29.220422734 x = 29.220422734 Simplifying x = 29.220422734Subproblem 2
x + -15.5 = -13.720422734 Simplifying x + -15.5 = -13.720422734 Reorder the terms: -15.5 + x = -13.720422734 Solving -15.5 + x = -13.720422734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = -13.720422734 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -13.720422734 + 15.5 x = -13.720422734 + 15.5 Combine like terms: -13.720422734 + 15.5 = 1.779577266 x = 1.779577266 Simplifying x = 1.779577266Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.220422734, 1.779577266}
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