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Simplifying 780 = x2 + 9x Reorder the terms: 780 = 9x + x2 Solving 780 = 9x + x2 Solving for variable 'x'. Reorder the terms: 780 + -9x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 780 + -9x + -1x2 = 0 + x2 + -1x2 780 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 780 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -780 + 9x + x2 = 0 Move the constant term to the right: Add '780' to each side of the equation. -780 + 9x + 780 + x2 = 0 + 780 Reorder the terms: -780 + 780 + 9x + x2 = 0 + 780 Combine like terms: -780 + 780 = 0 0 + 9x + x2 = 0 + 780 9x + x2 = 0 + 780 Combine like terms: 0 + 780 = 780 9x + x2 = 780 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 780 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 780 + 20.25 Combine like terms: 780 + 20.25 = 800.25 20.25 + 9x + x2 = 800.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 800.25 Calculate the square root of the right side: 28.28869032 Break this problem into two subproblems by setting (x + 4.5) equal to 28.28869032 and -28.28869032.Subproblem 1
x + 4.5 = 28.28869032 Simplifying x + 4.5 = 28.28869032 Reorder the terms: 4.5 + x = 28.28869032 Solving 4.5 + x = 28.28869032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 28.28869032 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 28.28869032 + -4.5 x = 28.28869032 + -4.5 Combine like terms: 28.28869032 + -4.5 = 23.78869032 x = 23.78869032 Simplifying x = 23.78869032Subproblem 2
x + 4.5 = -28.28869032 Simplifying x + 4.5 = -28.28869032 Reorder the terms: 4.5 + x = -28.28869032 Solving 4.5 + x = -28.28869032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -28.28869032 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -28.28869032 + -4.5 x = -28.28869032 + -4.5 Combine like terms: -28.28869032 + -4.5 = -32.78869032 x = -32.78869032 Simplifying x = -32.78869032Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.78869032, -32.78869032}
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