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Simplifying x2 + -25x + -12 = 0 Reorder the terms: -12 + -25x + x2 = 0 Solving -12 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -25x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -25x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -25x + x2 = 0 + 12 -25x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -25x + x2 = 12 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 = 12 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 12 + 156.25 Combine like terms: 12 + 156.25 = 168.25 156.25 + -25x + x2 = 168.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 168.25 Calculate the square root of the right side: 12.971121771 Break this problem into two subproblems by setting (x + -12.5) equal to 12.971121771 and -12.971121771.Subproblem 1
x + -12.5 = 12.971121771 Simplifying x + -12.5 = 12.971121771 Reorder the terms: -12.5 + x = 12.971121771 Solving -12.5 + x = 12.971121771 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 = 12.971121771 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.971121771 + 12.5 x = 12.971121771 + 12.5 Combine like terms: 12.971121771 + 12.5 = 25.471121771 x = 25.471121771 Simplifying x = 25.471121771Subproblem 2
x + -12.5 = -12.971121771 Simplifying x + -12.5 = -12.971121771 Reorder the terms: -12.5 + x = -12.971121771 Solving -12.5 + x = -12.971121771 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 = -12.971121771 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.971121771 + 12.5 x = -12.971121771 + 12.5 Combine like terms: -12.971121771 + 12.5 = -0.471121771 x = -0.471121771 Simplifying x = -0.471121771Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.471121771, -0.471121771}
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