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Simplifying 780 = x2 + x Reorder the terms: 780 = x + x2 Solving 780 = x + x2 Solving for variable 'x'. Reorder the terms: 780 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 780 + -1x + -1x2 = 0 + x2 + -1x2 780 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 780 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -780 + x + x2 = 0 Move the constant term to the right: Add '780' to each side of the equation. -780 + x + 780 + x2 = 0 + 780 Reorder the terms: -780 + 780 + x + x2 = 0 + 780 Combine like terms: -780 + 780 = 0 0 + x + x2 = 0 + 780 x + x2 = 0 + 780 Combine like terms: 0 + 780 = 780 x + x2 = 780 The x term is x. 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. + 0.25 + x2 = 780 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 780 + 0.25 Combine like terms: 780 + 0.25 = 780.25 1.25 + x2 = 780.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 780.25 Calculate the square root of the right side: 27.932955447 Break this problem into two subproblems by setting (x + 0.5) equal to 27.932955447 and -27.932955447.Subproblem 1
x + 0.5 = 27.932955447 Simplifying x + 0.5 = 27.932955447 Reorder the terms: 0.5 + x = 27.932955447 Solving 0.5 + x = 27.932955447 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 = 27.932955447 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 27.932955447 + -0.5 x = 27.932955447 + -0.5 Combine like terms: 27.932955447 + -0.5 = 27.432955447 x = 27.432955447 Simplifying x = 27.432955447Subproblem 2
x + 0.5 = -27.932955447 Simplifying x + 0.5 = -27.932955447 Reorder the terms: 0.5 + x = -27.932955447 Solving 0.5 + x = -27.932955447 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 = -27.932955447 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -27.932955447 + -0.5 x = -27.932955447 + -0.5 Combine like terms: -27.932955447 + -0.5 = -28.432955447 x = -28.432955447 Simplifying x = -28.432955447Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.432955447, -28.432955447}
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