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Simplifying x2 + -10x + -400 = 386 Reorder the terms: -400 + -10x + x2 = 386 Solving -400 + -10x + x2 = 386 Solving for variable 'x'. Reorder the terms: -400 + -386 + -10x + x2 = 386 + -386 Combine like terms: -400 + -386 = -786 -786 + -10x + x2 = 386 + -386 Combine like terms: 386 + -386 = 0 -786 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '786' to each side of the equation. -786 + -10x + 786 + x2 = 0 + 786 Reorder the terms: -786 + 786 + -10x + x2 = 0 + 786 Combine like terms: -786 + 786 = 0 0 + -10x + x2 = 0 + 786 -10x + x2 = 0 + 786 Combine like terms: 0 + 786 = 786 -10x + x2 = 786 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 786 + 25 Reorder the terms: 25 + -10x + x2 = 786 + 25 Combine like terms: 786 + 25 = 811 25 + -10x + x2 = 811 Factor a perfect square on the left side: (x + -5)(x + -5) = 811 Calculate the square root of the right side: 28.478061732 Break this problem into two subproblems by setting (x + -5) equal to 28.478061732 and -28.478061732.Subproblem 1
x + -5 = 28.478061732 Simplifying x + -5 = 28.478061732 Reorder the terms: -5 + x = 28.478061732 Solving -5 + x = 28.478061732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 28.478061732 + 5 Combine like terms: -5 + 5 = 0 0 + x = 28.478061732 + 5 x = 28.478061732 + 5 Combine like terms: 28.478061732 + 5 = 33.478061732 x = 33.478061732 Simplifying x = 33.478061732Subproblem 2
x + -5 = -28.478061732 Simplifying x + -5 = -28.478061732 Reorder the terms: -5 + x = -28.478061732 Solving -5 + x = -28.478061732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -28.478061732 + 5 Combine like terms: -5 + 5 = 0 0 + x = -28.478061732 + 5 x = -28.478061732 + 5 Combine like terms: -28.478061732 + 5 = -23.478061732 x = -23.478061732 Simplifying x = -23.478061732Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.478061732, -23.478061732}
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