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Simplifying x2 + -130x + 1050 = 0 Reorder the terms: 1050 + -130x + x2 = 0 Solving 1050 + -130x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1050' to each side of the equation. 1050 + -130x + -1050 + x2 = 0 + -1050 Reorder the terms: 1050 + -1050 + -130x + x2 = 0 + -1050 Combine like terms: 1050 + -1050 = 0 0 + -130x + x2 = 0 + -1050 -130x + x2 = 0 + -1050 Combine like terms: 0 + -1050 = -1050 -130x + x2 = -1050 The x term is -130x. Take half its coefficient (-65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. -130x + 4225 + x2 = -1050 + 4225 Reorder the terms: 4225 + -130x + x2 = -1050 + 4225 Combine like terms: -1050 + 4225 = 3175 4225 + -130x + x2 = 3175 Factor a perfect square on the left side: (x + -65)(x + -65) = 3175 Calculate the square root of the right side: 56.347138348 Break this problem into two subproblems by setting (x + -65) equal to 56.347138348 and -56.347138348.Subproblem 1
x + -65 = 56.347138348 Simplifying x + -65 = 56.347138348 Reorder the terms: -65 + x = 56.347138348 Solving -65 + x = 56.347138348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = 56.347138348 + 65 Combine like terms: -65 + 65 = 0 0 + x = 56.347138348 + 65 x = 56.347138348 + 65 Combine like terms: 56.347138348 + 65 = 121.347138348 x = 121.347138348 Simplifying x = 121.347138348Subproblem 2
x + -65 = -56.347138348 Simplifying x + -65 = -56.347138348 Reorder the terms: -65 + x = -56.347138348 Solving -65 + x = -56.347138348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = -56.347138348 + 65 Combine like terms: -65 + 65 = 0 0 + x = -56.347138348 + 65 x = -56.347138348 + 65 Combine like terms: -56.347138348 + 65 = 8.652861652 x = 8.652861652 Simplifying x = 8.652861652Solution
The solution to the problem is based on the solutions from the subproblems. x = {121.347138348, 8.652861652}
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