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Simplifying x2 + 130x + 800 = 0 Reorder the terms: 800 + 130x + x2 = 0 Solving 800 + 130x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-800' to each side of the equation. 800 + 130x + -800 + x2 = 0 + -800 Reorder the terms: 800 + -800 + 130x + x2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + 130x + x2 = 0 + -800 130x + x2 = 0 + -800 Combine like terms: 0 + -800 = -800 130x + x2 = -800 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 = -800 + 4225 Reorder the terms: 4225 + 130x + x2 = -800 + 4225 Combine like terms: -800 + 4225 = 3425 4225 + 130x + x2 = 3425 Factor a perfect square on the left side: (x + 65)(x + 65) = 3425 Calculate the square root of the right side: 58.523499554 Break this problem into two subproblems by setting (x + 65) equal to 58.523499554 and -58.523499554.Subproblem 1
x + 65 = 58.523499554 Simplifying x + 65 = 58.523499554 Reorder the terms: 65 + x = 58.523499554 Solving 65 + x = 58.523499554 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 = 58.523499554 + -65 Combine like terms: 65 + -65 = 0 0 + x = 58.523499554 + -65 x = 58.523499554 + -65 Combine like terms: 58.523499554 + -65 = -6.476500446 x = -6.476500446 Simplifying x = -6.476500446Subproblem 2
x + 65 = -58.523499554 Simplifying x + 65 = -58.523499554 Reorder the terms: 65 + x = -58.523499554 Solving 65 + x = -58.523499554 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 = -58.523499554 + -65 Combine like terms: 65 + -65 = 0 0 + x = -58.523499554 + -65 x = -58.523499554 + -65 Combine like terms: -58.523499554 + -65 = -123.523499554 x = -123.523499554 Simplifying x = -123.523499554Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.476500446, -123.523499554}
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