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Simplifying x2 + -5x + -210 = 0 Reorder the terms: -210 + -5x + x2 = 0 Solving -210 + -5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '210' to each side of the equation. -210 + -5x + 210 + x2 = 0 + 210 Reorder the terms: -210 + 210 + -5x + x2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + -5x + x2 = 0 + 210 -5x + x2 = 0 + 210 Combine like terms: 0 + 210 = 210 -5x + x2 = 210 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 210 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 210 + 6.25 Combine like terms: 210 + 6.25 = 216.25 6.25 + -5x + x2 = 216.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 216.25 Calculate the square root of the right side: 14.70544117 Break this problem into two subproblems by setting (x + -2.5) equal to 14.70544117 and -14.70544117.Subproblem 1
x + -2.5 = 14.70544117 Simplifying x + -2.5 = 14.70544117 Reorder the terms: -2.5 + x = 14.70544117 Solving -2.5 + x = 14.70544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 14.70544117 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 14.70544117 + 2.5 x = 14.70544117 + 2.5 Combine like terms: 14.70544117 + 2.5 = 17.20544117 x = 17.20544117 Simplifying x = 17.20544117Subproblem 2
x + -2.5 = -14.70544117 Simplifying x + -2.5 = -14.70544117 Reorder the terms: -2.5 + x = -14.70544117 Solving -2.5 + x = -14.70544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -14.70544117 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -14.70544117 + 2.5 x = -14.70544117 + 2.5 Combine like terms: -14.70544117 + 2.5 = -12.20544117 x = -12.20544117 Simplifying x = -12.20544117Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.20544117, -12.20544117}
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