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Simplifying x2 + 60x + 600 = 1064 Reorder the terms: 600 + 60x + x2 = 1064 Solving 600 + 60x + x2 = 1064 Solving for variable 'x'. Reorder the terms: 600 + -1064 + 60x + x2 = 1064 + -1064 Combine like terms: 600 + -1064 = -464 -464 + 60x + x2 = 1064 + -1064 Combine like terms: 1064 + -1064 = 0 -464 + 60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '464' to each side of the equation. -464 + 60x + 464 + x2 = 0 + 464 Reorder the terms: -464 + 464 + 60x + x2 = 0 + 464 Combine like terms: -464 + 464 = 0 0 + 60x + x2 = 0 + 464 60x + x2 = 0 + 464 Combine like terms: 0 + 464 = 464 60x + x2 = 464 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = 464 + 900 Reorder the terms: 900 + 60x + x2 = 464 + 900 Combine like terms: 464 + 900 = 1364 900 + 60x + x2 = 1364 Factor a perfect square on the left side: (x + 30)(x + 30) = 1364 Calculate the square root of the right side: 36.932370625 Break this problem into two subproblems by setting (x + 30) equal to 36.932370625 and -36.932370625.Subproblem 1
x + 30 = 36.932370625 Simplifying x + 30 = 36.932370625 Reorder the terms: 30 + x = 36.932370625 Solving 30 + x = 36.932370625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 36.932370625 + -30 Combine like terms: 30 + -30 = 0 0 + x = 36.932370625 + -30 x = 36.932370625 + -30 Combine like terms: 36.932370625 + -30 = 6.932370625 x = 6.932370625 Simplifying x = 6.932370625Subproblem 2
x + 30 = -36.932370625 Simplifying x + 30 = -36.932370625 Reorder the terms: 30 + x = -36.932370625 Solving 30 + x = -36.932370625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -36.932370625 + -30 Combine like terms: 30 + -30 = 0 0 + x = -36.932370625 + -30 x = -36.932370625 + -30 Combine like terms: -36.932370625 + -30 = -66.932370625 x = -66.932370625 Simplifying x = -66.932370625Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.932370625, -66.932370625}
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