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Simplifying (x)(x + -25) = 156 Reorder the terms: x(-25 + x) = 156 (-25 * x + x * x) = 156 (-25x + x2) = 156 Solving -25x + x2 = 156 Solving for variable 'x'. Reorder the terms: -156 + -25x + x2 = 156 + -156 Combine like terms: 156 + -156 = 0 -156 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '156' to each side of the equation. -156 + -25x + 156 + x2 = 0 + 156 Reorder the terms: -156 + 156 + -25x + x2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + -25x + x2 = 0 + 156 -25x + x2 = 0 + 156 Combine like terms: 0 + 156 = 156 -25x + x2 = 156 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 156 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 156 + 156.25 Combine like terms: 156 + 156.25 = 312.25 156.25 + -25x + x2 = 312.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 312.25 Calculate the square root of the right side: 17.670597047 Break this problem into two subproblems by setting (x + -12.5) equal to 17.670597047 and -17.670597047.Subproblem 1
x + -12.5 = 17.670597047 Simplifying x + -12.5 = 17.670597047 Reorder the terms: -12.5 + x = 17.670597047 Solving -12.5 + x = 17.670597047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 17.670597047 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 17.670597047 + 12.5 x = 17.670597047 + 12.5 Combine like terms: 17.670597047 + 12.5 = 30.170597047 x = 30.170597047 Simplifying x = 30.170597047Subproblem 2
x + -12.5 = -17.670597047 Simplifying x + -12.5 = -17.670597047 Reorder the terms: -12.5 + x = -17.670597047 Solving -12.5 + x = -17.670597047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -17.670597047 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -17.670597047 + 12.5 x = -17.670597047 + 12.5 Combine like terms: -17.670597047 + 12.5 = -5.170597047 x = -5.170597047 Simplifying x = -5.170597047Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.170597047, -5.170597047}
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