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Simplifying x(x + -12) = 1000 Reorder the terms: x(-12 + x) = 1000 (-12 * x + x * x) = 1000 (-12x + x2) = 1000 Solving -12x + x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + -12x + x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -12x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -12x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -12x + x2 = 0 + 1000 -12x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -12x + x2 = 1000 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 1000 + 36 Reorder the terms: 36 + -12x + x2 = 1000 + 36 Combine like terms: 1000 + 36 = 1036 36 + -12x + x2 = 1036 Factor a perfect square on the left side: (x + -6)(x + -6) = 1036 Calculate the square root of the right side: 32.186953879 Break this problem into two subproblems by setting (x + -6) equal to 32.186953879 and -32.186953879.Subproblem 1
x + -6 = 32.186953879 Simplifying x + -6 = 32.186953879 Reorder the terms: -6 + x = 32.186953879 Solving -6 + x = 32.186953879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 32.186953879 + 6 Combine like terms: -6 + 6 = 0 0 + x = 32.186953879 + 6 x = 32.186953879 + 6 Combine like terms: 32.186953879 + 6 = 38.186953879 x = 38.186953879 Simplifying x = 38.186953879Subproblem 2
x + -6 = -32.186953879 Simplifying x + -6 = -32.186953879 Reorder the terms: -6 + x = -32.186953879 Solving -6 + x = -32.186953879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -32.186953879 + 6 Combine like terms: -6 + 6 = 0 0 + x = -32.186953879 + 6 x = -32.186953879 + 6 Combine like terms: -32.186953879 + 6 = -26.186953879 x = -26.186953879 Simplifying x = -26.186953879Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.186953879, -26.186953879}
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