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Simplifying 500 + 60x + -1x2 = 0 Solving 500 + 60x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -500 + -60x + x2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + -60x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -60x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -60x + x2 = 0 + 500 -60x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -60x + x2 = 500 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 = 500 + 900 Reorder the terms: 900 + -60x + x2 = 500 + 900 Combine like terms: 500 + 900 = 1400 900 + -60x + x2 = 1400 Factor a perfect square on the left side: (x + -30)(x + -30) = 1400 Calculate the square root of the right side: 37.416573868 Break this problem into two subproblems by setting (x + -30) equal to 37.416573868 and -37.416573868.Subproblem 1
x + -30 = 37.416573868 Simplifying x + -30 = 37.416573868 Reorder the terms: -30 + x = 37.416573868 Solving -30 + x = 37.416573868 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 = 37.416573868 + 30 Combine like terms: -30 + 30 = 0 0 + x = 37.416573868 + 30 x = 37.416573868 + 30 Combine like terms: 37.416573868 + 30 = 67.416573868 x = 67.416573868 Simplifying x = 67.416573868Subproblem 2
x + -30 = -37.416573868 Simplifying x + -30 = -37.416573868 Reorder the terms: -30 + x = -37.416573868 Solving -30 + x = -37.416573868 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 = -37.416573868 + 30 Combine like terms: -30 + 30 = 0 0 + x = -37.416573868 + 30 x = -37.416573868 + 30 Combine like terms: -37.416573868 + 30 = -7.416573868 x = -7.416573868 Simplifying x = -7.416573868Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.416573868, -7.416573868}
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