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Simplifying -1x2 + 10x + -25x + 2x2 + -18x + -40 = 0 Reorder the terms: -40 + 10x + -25x + -18x + -1x2 + 2x2 = 0 Combine like terms: 10x + -25x = -15x -40 + -15x + -18x + -1x2 + 2x2 = 0 Combine like terms: -15x + -18x = -33x -40 + -33x + -1x2 + 2x2 = 0 Combine like terms: -1x2 + 2x2 = 1x2 -40 + -33x + 1x2 = 0 Solving -40 + -33x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -33x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -33x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -33x + x2 = 0 + 40 -33x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -33x + x2 = 40 The x term is -33x. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33x + 272.25 + x2 = 40 + 272.25 Reorder the terms: 272.25 + -33x + x2 = 40 + 272.25 Combine like terms: 40 + 272.25 = 312.25 272.25 + -33x + x2 = 312.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 312.25 Calculate the square root of the right side: 17.670597047 Break this problem into two subproblems by setting (x + -16.5) equal to 17.670597047 and -17.670597047.Subproblem 1
x + -16.5 = 17.670597047 Simplifying x + -16.5 = 17.670597047 Reorder the terms: -16.5 + x = 17.670597047 Solving -16.5 + x = 17.670597047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = 17.670597047 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 17.670597047 + 16.5 x = 17.670597047 + 16.5 Combine like terms: 17.670597047 + 16.5 = 34.170597047 x = 34.170597047 Simplifying x = 34.170597047Subproblem 2
x + -16.5 = -17.670597047 Simplifying x + -16.5 = -17.670597047 Reorder the terms: -16.5 + x = -17.670597047 Solving -16.5 + x = -17.670597047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = -17.670597047 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -17.670597047 + 16.5 x = -17.670597047 + 16.5 Combine like terms: -17.670597047 + 16.5 = -1.170597047 x = -1.170597047 Simplifying x = -1.170597047Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.170597047, -1.170597047}
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