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Simplifying x2 + -2x + x2 = 421 Reorder the terms: -2x + x2 + x2 = 421 Combine like terms: x2 + x2 = 2x2 -2x + 2x2 = 421 Solving -2x + 2x2 = 421 Solving for variable 'x'. Reorder the terms: -421 + -2x + 2x2 = 421 + -421 Combine like terms: 421 + -421 = 0 -421 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -210.5 + -1x + x2 = 0 Move the constant term to the right: Add '210.5' to each side of the equation. -210.5 + -1x + 210.5 + x2 = 0 + 210.5 Reorder the terms: -210.5 + 210.5 + -1x + x2 = 0 + 210.5 Combine like terms: -210.5 + 210.5 = 0.0 0.0 + -1x + x2 = 0 + 210.5 -1x + x2 = 0 + 210.5 Combine like terms: 0 + 210.5 = 210.5 -1x + x2 = 210.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 210.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 210.5 + 0.25 Combine like terms: 210.5 + 0.25 = 210.75 0.25 + -1x + x2 = 210.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 210.75 Calculate the square root of the right side: 14.517231141 Break this problem into two subproblems by setting (x + -0.5) equal to 14.517231141 and -14.517231141.Subproblem 1
x + -0.5 = 14.517231141 Simplifying x + -0.5 = 14.517231141 Reorder the terms: -0.5 + x = 14.517231141 Solving -0.5 + x = 14.517231141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 14.517231141 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 14.517231141 + 0.5 x = 14.517231141 + 0.5 Combine like terms: 14.517231141 + 0.5 = 15.017231141 x = 15.017231141 Simplifying x = 15.017231141Subproblem 2
x + -0.5 = -14.517231141 Simplifying x + -0.5 = -14.517231141 Reorder the terms: -0.5 + x = -14.517231141 Solving -0.5 + x = -14.517231141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -14.517231141 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -14.517231141 + 0.5 x = -14.517231141 + 0.5 Combine like terms: -14.517231141 + 0.5 = -14.017231141 x = -14.017231141 Simplifying x = -14.017231141Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.017231141, -14.017231141}
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