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Simplifying (4 * 4 * 4 * 4 * 4X + 3X + -12) + -1(3 * 3 * 3 + X * X + -3X + -7) = 0 Multiply 4 * 4 (16 * 4 * 4 * 4X + 3X + -12) + -1(3 * 3 * 3 + X * X + -3X + -7) = 0 Multiply 16 * 4 (64 * 4 * 4X + 3X + -12) + -1(3 * 3 * 3 + X * X + -3X + -7) = 0 Multiply 64 * 4 (256 * 4X + 3X + -12) + -1(3 * 3 * 3 + X * X + -3X + -7) = 0 Multiply 256 * 4 (1024X + 3X + -12) + -1(3 * 3 * 3 + X * X + -3X + -7) = 0 Reorder the terms: (-12 + 1024X + 3X) + -1(3 * 3 * 3 + X * X + -3X + -7) = 0 Combine like terms: 1024X + 3X = 1027X (-12 + 1027X) + -1(3 * 3 * 3 + X * X + -3X + -7) = 0 Remove parenthesis around (-12 + 1027X) -12 + 1027X + -1(3 * 3 * 3 + X * X + -3X + -7) = 0 Multiply 3 * 3 -12 + 1027X + -1(9 * 3 + X * X + -3X + -7) = 0 Multiply 9 * 3 -12 + 1027X + -1(27 + X * X + -3X + -7) = 0 Multiply X * X -12 + 1027X + -1(27 + X2 + -3X + -7) = 0 Reorder the terms: -12 + 1027X + -1(27 + -7 + -3X + X2) = 0 Combine like terms: 27 + -7 = 20 -12 + 1027X + -1(20 + -3X + X2) = 0 -12 + 1027X + (20 * -1 + -3X * -1 + X2 * -1) = 0 -12 + 1027X + (-20 + 3X + -1X2) = 0 Reorder the terms: -12 + -20 + 1027X + 3X + -1X2 = 0 Combine like terms: -12 + -20 = -32 -32 + 1027X + 3X + -1X2 = 0 Combine like terms: 1027X + 3X = 1030X -32 + 1030X + -1X2 = 0 Solving -32 + 1030X + -1X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 32 + -1030X + X2 = 0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + -1030X + -32 + X2 = 0 + -32 Reorder the terms: 32 + -32 + -1030X + X2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -1030X + X2 = 0 + -32 -1030X + X2 = 0 + -32 Combine like terms: 0 + -32 = -32 -1030X + X2 = -32 The X term is -1030X. Take half its coefficient (-515). Square it (265225) and add it to both sides. Add '265225' to each side of the equation. -1030X + 265225 + X2 = -32 + 265225 Reorder the terms: 265225 + -1030X + X2 = -32 + 265225 Combine like terms: -32 + 265225 = 265193 265225 + -1030X + X2 = 265193 Factor a perfect square on the left side: (X + -515)(X + -515) = 265193 Calculate the square root of the right side: 514.968931102 Break this problem into two subproblems by setting (X + -515) equal to 514.968931102 and -514.968931102.Subproblem 1
X + -515 = 514.968931102 Simplifying X + -515 = 514.968931102 Reorder the terms: -515 + X = 514.968931102 Solving -515 + X = 514.968931102 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '515' to each side of the equation. -515 + 515 + X = 514.968931102 + 515 Combine like terms: -515 + 515 = 0 0 + X = 514.968931102 + 515 X = 514.968931102 + 515 Combine like terms: 514.968931102 + 515 = 1029.968931102 X = 1029.968931102 Simplifying X = 1029.968931102Subproblem 2
X + -515 = -514.968931102 Simplifying X + -515 = -514.968931102 Reorder the terms: -515 + X = -514.968931102 Solving -515 + X = -514.968931102 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '515' to each side of the equation. -515 + 515 + X = -514.968931102 + 515 Combine like terms: -515 + 515 = 0 0 + X = -514.968931102 + 515 X = -514.968931102 + 515 Combine like terms: -514.968931102 + 515 = 0.031068898 X = 0.031068898 Simplifying X = 0.031068898Solution
The solution to the problem is based on the solutions from the subproblems. X = {1029.968931102, 0.031068898}
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