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Simplifying -13x2 + 30x + 98 = 0 Reorder the terms: 98 + 30x + -13x2 = 0 Solving 98 + 30x + -13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -7.538461538 + -2.307692308x + x2 = 0 Move the constant term to the right: Add '7.538461538' to each side of the equation. -7.538461538 + -2.307692308x + 7.538461538 + x2 = 0 + 7.538461538 Reorder the terms: -7.538461538 + 7.538461538 + -2.307692308x + x2 = 0 + 7.538461538 Combine like terms: -7.538461538 + 7.538461538 = 0.000000000 0.000000000 + -2.307692308x + x2 = 0 + 7.538461538 -2.307692308x + x2 = 0 + 7.538461538 Combine like terms: 0 + 7.538461538 = 7.538461538 -2.307692308x + x2 = 7.538461538 The x term is -2.307692308x. Take half its coefficient (-1.153846154). Square it (1.331360947) and add it to both sides. Add '1.331360947' to each side of the equation. -2.307692308x + 1.331360947 + x2 = 7.538461538 + 1.331360947 Reorder the terms: 1.331360947 + -2.307692308x + x2 = 7.538461538 + 1.331360947 Combine like terms: 7.538461538 + 1.331360947 = 8.869822485 1.331360947 + -2.307692308x + x2 = 8.869822485 Factor a perfect square on the left side: (x + -1.153846154)(x + -1.153846154) = 8.869822485 Calculate the square root of the right side: 2.97822472 Break this problem into two subproblems by setting (x + -1.153846154) equal to 2.97822472 and -2.97822472.Subproblem 1
x + -1.153846154 = 2.97822472 Simplifying x + -1.153846154 = 2.97822472 Reorder the terms: -1.153846154 + x = 2.97822472 Solving -1.153846154 + x = 2.97822472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.153846154' to each side of the equation. -1.153846154 + 1.153846154 + x = 2.97822472 + 1.153846154 Combine like terms: -1.153846154 + 1.153846154 = 0.000000000 0.000000000 + x = 2.97822472 + 1.153846154 x = 2.97822472 + 1.153846154 Combine like terms: 2.97822472 + 1.153846154 = 4.132070874 x = 4.132070874 Simplifying x = 4.132070874Subproblem 2
x + -1.153846154 = -2.97822472 Simplifying x + -1.153846154 = -2.97822472 Reorder the terms: -1.153846154 + x = -2.97822472 Solving -1.153846154 + x = -2.97822472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.153846154' to each side of the equation. -1.153846154 + 1.153846154 + x = -2.97822472 + 1.153846154 Combine like terms: -1.153846154 + 1.153846154 = 0.000000000 0.000000000 + x = -2.97822472 + 1.153846154 x = -2.97822472 + 1.153846154 Combine like terms: -2.97822472 + 1.153846154 = -1.824378566 x = -1.824378566 Simplifying x = -1.824378566Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.132070874, -1.824378566}
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