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Simplifying x2 + -25x + -75 = 0 Reorder the terms: -75 + -25x + x2 = 0 Solving -75 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + -25x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + -25x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -25x + x2 = 0 + 75 -25x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 -25x + x2 = 75 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 = 75 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 75 + 156.25 Combine like terms: 75 + 156.25 = 231.25 156.25 + -25x + x2 = 231.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 231.25 Calculate the square root of the right side: 15.206906326 Break this problem into two subproblems by setting (x + -12.5) equal to 15.206906326 and -15.206906326.Subproblem 1
x + -12.5 = 15.206906326 Simplifying x + -12.5 = 15.206906326 Reorder the terms: -12.5 + x = 15.206906326 Solving -12.5 + x = 15.206906326 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 = 15.206906326 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 15.206906326 + 12.5 x = 15.206906326 + 12.5 Combine like terms: 15.206906326 + 12.5 = 27.706906326 x = 27.706906326 Simplifying x = 27.706906326Subproblem 2
x + -12.5 = -15.206906326 Simplifying x + -12.5 = -15.206906326 Reorder the terms: -12.5 + x = -15.206906326 Solving -12.5 + x = -15.206906326 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 = -15.206906326 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -15.206906326 + 12.5 x = -15.206906326 + 12.5 Combine like terms: -15.206906326 + 12.5 = -2.706906326 x = -2.706906326 Simplifying x = -2.706906326Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.706906326, -2.706906326}
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