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Simplifying -0.2x2 + 12.6x + 200 = 0 Reorder the terms: 200 + 12.6x + -0.2x2 = 0 Solving 200 + 12.6x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -1000 + -63x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -63x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -63x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -63x + x2 = 0 + 1000 -63x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -63x + x2 = 1000 The x term is -63x. Take half its coefficient (-31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. -63x + 992.25 + x2 = 1000 + 992.25 Reorder the terms: 992.25 + -63x + x2 = 1000 + 992.25 Combine like terms: 1000 + 992.25 = 1992.25 992.25 + -63x + x2 = 1992.25 Factor a perfect square on the left side: (x + -31.5)(x + -31.5) = 1992.25 Calculate the square root of the right side: 44.634627813 Break this problem into two subproblems by setting (x + -31.5) equal to 44.634627813 and -44.634627813.Subproblem 1
x + -31.5 = 44.634627813 Simplifying x + -31.5 = 44.634627813 Reorder the terms: -31.5 + x = 44.634627813 Solving -31.5 + x = 44.634627813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.5' to each side of the equation. -31.5 + 31.5 + x = 44.634627813 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + x = 44.634627813 + 31.5 x = 44.634627813 + 31.5 Combine like terms: 44.634627813 + 31.5 = 76.134627813 x = 76.134627813 Simplifying x = 76.134627813Subproblem 2
x + -31.5 = -44.634627813 Simplifying x + -31.5 = -44.634627813 Reorder the terms: -31.5 + x = -44.634627813 Solving -31.5 + x = -44.634627813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.5' to each side of the equation. -31.5 + 31.5 + x = -44.634627813 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + x = -44.634627813 + 31.5 x = -44.634627813 + 31.5 Combine like terms: -44.634627813 + 31.5 = -13.134627813 x = -13.134627813 Simplifying x = -13.134627813Solution
The solution to the problem is based on the solutions from the subproblems. x = {76.134627813, -13.134627813}
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