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Simplifying x2 + 130x + -225 = 0 Reorder the terms: -225 + 130x + x2 = 0 Solving -225 + 130x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 130x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 130x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 130x + x2 = 0 + 225 130x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 130x + x2 = 225 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 = 225 + 4225 Reorder the terms: 4225 + 130x + x2 = 225 + 4225 Combine like terms: 225 + 4225 = 4450 4225 + 130x + x2 = 4450 Factor a perfect square on the left side: (x + 65)(x + 65) = 4450 Calculate the square root of the right side: 66.708320321 Break this problem into two subproblems by setting (x + 65) equal to 66.708320321 and -66.708320321.Subproblem 1
x + 65 = 66.708320321 Simplifying x + 65 = 66.708320321 Reorder the terms: 65 + x = 66.708320321 Solving 65 + x = 66.708320321 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 = 66.708320321 + -65 Combine like terms: 65 + -65 = 0 0 + x = 66.708320321 + -65 x = 66.708320321 + -65 Combine like terms: 66.708320321 + -65 = 1.708320321 x = 1.708320321 Simplifying x = 1.708320321Subproblem 2
x + 65 = -66.708320321 Simplifying x + 65 = -66.708320321 Reorder the terms: 65 + x = -66.708320321 Solving 65 + x = -66.708320321 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 = -66.708320321 + -65 Combine like terms: 65 + -65 = 0 0 + x = -66.708320321 + -65 x = -66.708320321 + -65 Combine like terms: -66.708320321 + -65 = -131.708320321 x = -131.708320321 Simplifying x = -131.708320321Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.708320321, -131.708320321}
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