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Simplifying x2 + -8x + -418 = 0 Reorder the terms: -418 + -8x + x2 = 0 Solving -418 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '418' to each side of the equation. -418 + -8x + 418 + x2 = 0 + 418 Reorder the terms: -418 + 418 + -8x + x2 = 0 + 418 Combine like terms: -418 + 418 = 0 0 + -8x + x2 = 0 + 418 -8x + x2 = 0 + 418 Combine like terms: 0 + 418 = 418 -8x + x2 = 418 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 418 + 16 Reorder the terms: 16 + -8x + x2 = 418 + 16 Combine like terms: 418 + 16 = 434 16 + -8x + x2 = 434 Factor a perfect square on the left side: (x + -4)(x + -4) = 434 Calculate the square root of the right side: 20.832666656 Break this problem into two subproblems by setting (x + -4) equal to 20.832666656 and -20.832666656.Subproblem 1
x + -4 = 20.832666656 Simplifying x + -4 = 20.832666656 Reorder the terms: -4 + x = 20.832666656 Solving -4 + x = 20.832666656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 20.832666656 + 4 Combine like terms: -4 + 4 = 0 0 + x = 20.832666656 + 4 x = 20.832666656 + 4 Combine like terms: 20.832666656 + 4 = 24.832666656 x = 24.832666656 Simplifying x = 24.832666656Subproblem 2
x + -4 = -20.832666656 Simplifying x + -4 = -20.832666656 Reorder the terms: -4 + x = -20.832666656 Solving -4 + x = -20.832666656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -20.832666656 + 4 Combine like terms: -4 + 4 = 0 0 + x = -20.832666656 + 4 x = -20.832666656 + 4 Combine like terms: -20.832666656 + 4 = -16.832666656 x = -16.832666656 Simplifying x = -16.832666656Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.832666656, -16.832666656}
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