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Simplifying -0.5x2 + 12.5x + 1.9 = 0 Reorder the terms: 1.9 + 12.5x + -0.5x2 = 0 Solving 1.9 + 12.5x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -3.8 + -25x + x2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + -25x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + -25x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + -25x + x2 = 0 + 3.8 -25x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 -25x + x2 = 3.8 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 = 3.8 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 3.8 + 156.25 Combine like terms: 3.8 + 156.25 = 160.05 156.25 + -25x + x2 = 160.05 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 160.05 Calculate the square root of the right side: 12.65108691 Break this problem into two subproblems by setting (x + -12.5) equal to 12.65108691 and -12.65108691.Subproblem 1
x + -12.5 = 12.65108691 Simplifying x + -12.5 = 12.65108691 Reorder the terms: -12.5 + x = 12.65108691 Solving -12.5 + x = 12.65108691 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 = 12.65108691 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.65108691 + 12.5 x = 12.65108691 + 12.5 Combine like terms: 12.65108691 + 12.5 = 25.15108691 x = 25.15108691 Simplifying x = 25.15108691Subproblem 2
x + -12.5 = -12.65108691 Simplifying x + -12.5 = -12.65108691 Reorder the terms: -12.5 + x = -12.65108691 Solving -12.5 + x = -12.65108691 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 = -12.65108691 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.65108691 + 12.5 x = -12.65108691 + 12.5 Combine like terms: -12.65108691 + 12.5 = -0.15108691 x = -0.15108691 Simplifying x = -0.15108691Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.15108691, -0.15108691}
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