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Simplifying (5X2 + -7X + -21) + (6X2 + 9X) = 0 Reorder the terms: (-21 + -7X + 5X2) + (6X2 + 9X) = 0 Remove parenthesis around (-21 + -7X + 5X2) -21 + -7X + 5X2 + (6X2 + 9X) = 0 Reorder the terms: -21 + -7X + 5X2 + (9X + 6X2) = 0 Remove parenthesis around (9X + 6X2) -21 + -7X + 5X2 + 9X + 6X2 = 0 Reorder the terms: -21 + -7X + 9X + 5X2 + 6X2 = 0 Combine like terms: -7X + 9X = 2X -21 + 2X + 5X2 + 6X2 = 0 Combine like terms: 5X2 + 6X2 = 11X2 -21 + 2X + 11X2 = 0 Solving -21 + 2X + 11X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.909090909 + 0.1818181818X + X2 = 0 Move the constant term to the right: Add '1.909090909' to each side of the equation. -1.909090909 + 0.1818181818X + 1.909090909 + X2 = 0 + 1.909090909 Reorder the terms: -1.909090909 + 1.909090909 + 0.1818181818X + X2 = 0 + 1.909090909 Combine like terms: -1.909090909 + 1.909090909 = 0.000000000 0.000000000 + 0.1818181818X + X2 = 0 + 1.909090909 0.1818181818X + X2 = 0 + 1.909090909 Combine like terms: 0 + 1.909090909 = 1.909090909 0.1818181818X + X2 = 1.909090909 The X term is 0.1818181818X. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818X + 0.008264462808 + X2 = 1.909090909 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818X + X2 = 1.909090909 + 0.008264462808 Combine like terms: 1.909090909 + 0.008264462808 = 1.917355371808 0.008264462808 + 0.1818181818X + X2 = 1.917355371808 Factor a perfect square on the left side: (X + 0.0909090909)(X + 0.0909090909) = 1.917355371808 Calculate the square root of the right side: 1.384686019 Break this problem into two subproblems by setting (X + 0.0909090909) equal to 1.384686019 and -1.384686019.Subproblem 1
X + 0.0909090909 = 1.384686019 Simplifying X + 0.0909090909 = 1.384686019 Reorder the terms: 0.0909090909 + X = 1.384686019 Solving 0.0909090909 + X = 1.384686019 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + X = 1.384686019 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + X = 1.384686019 + -0.0909090909 X = 1.384686019 + -0.0909090909 Combine like terms: 1.384686019 + -0.0909090909 = 1.2937769281 X = 1.2937769281 Simplifying X = 1.2937769281Subproblem 2
X + 0.0909090909 = -1.384686019 Simplifying X + 0.0909090909 = -1.384686019 Reorder the terms: 0.0909090909 + X = -1.384686019 Solving 0.0909090909 + X = -1.384686019 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + X = -1.384686019 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + X = -1.384686019 + -0.0909090909 X = -1.384686019 + -0.0909090909 Combine like terms: -1.384686019 + -0.0909090909 = -1.4755951099 X = -1.4755951099 Simplifying X = -1.4755951099Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.2937769281, -1.4755951099}
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