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Simplifying x2 + -25x + -3 = 0 Reorder the terms: -3 + -25x + x2 = 0 Solving -3 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -25x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -25x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -25x + x2 = 0 + 3 -25x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -25x + x2 = 3 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 = 3 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 3 + 156.25 Combine like terms: 3 + 156.25 = 159.25 156.25 + -25x + x2 = 159.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 159.25 Calculate the square root of the right side: 12.619429464 Break this problem into two subproblems by setting (x + -12.5) equal to 12.619429464 and -12.619429464.Subproblem 1
x + -12.5 = 12.619429464 Simplifying x + -12.5 = 12.619429464 Reorder the terms: -12.5 + x = 12.619429464 Solving -12.5 + x = 12.619429464 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 = 12.619429464 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.619429464 + 12.5 x = 12.619429464 + 12.5 Combine like terms: 12.619429464 + 12.5 = 25.119429464 x = 25.119429464 Simplifying x = 25.119429464Subproblem 2
x + -12.5 = -12.619429464 Simplifying x + -12.5 = -12.619429464 Reorder the terms: -12.5 + x = -12.619429464 Solving -12.5 + x = -12.619429464 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 = -12.619429464 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.619429464 + 12.5 x = -12.619429464 + 12.5 Combine like terms: -12.619429464 + 12.5 = -0.119429464 x = -0.119429464 Simplifying x = -0.119429464Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.119429464, -0.119429464}
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