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Simplifying x2 + -28x + -840 = 0 Reorder the terms: -840 + -28x + x2 = 0 Solving -840 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '840' to each side of the equation. -840 + -28x + 840 + x2 = 0 + 840 Reorder the terms: -840 + 840 + -28x + x2 = 0 + 840 Combine like terms: -840 + 840 = 0 0 + -28x + x2 = 0 + 840 -28x + x2 = 0 + 840 Combine like terms: 0 + 840 = 840 -28x + x2 = 840 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = 840 + 196 Reorder the terms: 196 + -28x + x2 = 840 + 196 Combine like terms: 840 + 196 = 1036 196 + -28x + x2 = 1036 Factor a perfect square on the left side: (x + -14)(x + -14) = 1036 Calculate the square root of the right side: 32.186953879 Break this problem into two subproblems by setting (x + -14) equal to 32.186953879 and -32.186953879.Subproblem 1
x + -14 = 32.186953879 Simplifying x + -14 = 32.186953879 Reorder the terms: -14 + x = 32.186953879 Solving -14 + x = 32.186953879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 32.186953879 + 14 Combine like terms: -14 + 14 = 0 0 + x = 32.186953879 + 14 x = 32.186953879 + 14 Combine like terms: 32.186953879 + 14 = 46.186953879 x = 46.186953879 Simplifying x = 46.186953879Subproblem 2
x + -14 = -32.186953879 Simplifying x + -14 = -32.186953879 Reorder the terms: -14 + x = -32.186953879 Solving -14 + x = -32.186953879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -32.186953879 + 14 Combine like terms: -14 + 14 = 0 0 + x = -32.186953879 + 14 x = -32.186953879 + 14 Combine like terms: -32.186953879 + 14 = -18.186953879 x = -18.186953879 Simplifying x = -18.186953879Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.186953879, -18.186953879}
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