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Simplifying x2 + -725 + -60x = 0 Reorder the terms: -725 + -60x + x2 = 0 Solving -725 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '725' to each side of the equation. -725 + -60x + 725 + x2 = 0 + 725 Reorder the terms: -725 + 725 + -60x + x2 = 0 + 725 Combine like terms: -725 + 725 = 0 0 + -60x + x2 = 0 + 725 -60x + x2 = 0 + 725 Combine like terms: 0 + 725 = 725 -60x + x2 = 725 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 = 725 + 900 Reorder the terms: 900 + -60x + x2 = 725 + 900 Combine like terms: 725 + 900 = 1625 900 + -60x + x2 = 1625 Factor a perfect square on the left side: (x + -30)(x + -30) = 1625 Calculate the square root of the right side: 40.311288741 Break this problem into two subproblems by setting (x + -30) equal to 40.311288741 and -40.311288741.Subproblem 1
x + -30 = 40.311288741 Simplifying x + -30 = 40.311288741 Reorder the terms: -30 + x = 40.311288741 Solving -30 + x = 40.311288741 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 = 40.311288741 + 30 Combine like terms: -30 + 30 = 0 0 + x = 40.311288741 + 30 x = 40.311288741 + 30 Combine like terms: 40.311288741 + 30 = 70.311288741 x = 70.311288741 Simplifying x = 70.311288741Subproblem 2
x + -30 = -40.311288741 Simplifying x + -30 = -40.311288741 Reorder the terms: -30 + x = -40.311288741 Solving -30 + x = -40.311288741 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 = -40.311288741 + 30 Combine like terms: -30 + 30 = 0 0 + x = -40.311288741 + 30 x = -40.311288741 + 30 Combine like terms: -40.311288741 + 30 = -10.311288741 x = -10.311288741 Simplifying x = -10.311288741Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.311288741, -10.311288741}
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