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Simplifying (13x2 + 7x + -15) + (8x2 + -15x + -9) = 0 Reorder the terms: (-15 + 7x + 13x2) + (8x2 + -15x + -9) = 0 Remove parenthesis around (-15 + 7x + 13x2) -15 + 7x + 13x2 + (8x2 + -15x + -9) = 0 Reorder the terms: -15 + 7x + 13x2 + (-9 + -15x + 8x2) = 0 Remove parenthesis around (-9 + -15x + 8x2) -15 + 7x + 13x2 + -9 + -15x + 8x2 = 0 Reorder the terms: -15 + -9 + 7x + -15x + 13x2 + 8x2 = 0 Combine like terms: -15 + -9 = -24 -24 + 7x + -15x + 13x2 + 8x2 = 0 Combine like terms: 7x + -15x = -8x -24 + -8x + 13x2 + 8x2 = 0 Combine like terms: 13x2 + 8x2 = 21x2 -24 + -8x + 21x2 = 0 Solving -24 + -8x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.142857143 + -0.380952381x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -0.380952381x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -0.380952381x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -0.380952381x + x2 = 0 + 1.142857143 -0.380952381x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -0.380952381x + x2 = 1.142857143 The x term is -0.380952381x. Take half its coefficient (-0.1904761905). Square it (0.03628117915) and add it to both sides. Add '0.03628117915' to each side of the equation. -0.380952381x + 0.03628117915 + x2 = 1.142857143 + 0.03628117915 Reorder the terms: 0.03628117915 + -0.380952381x + x2 = 1.142857143 + 0.03628117915 Combine like terms: 1.142857143 + 0.03628117915 = 1.17913832215 0.03628117915 + -0.380952381x + x2 = 1.17913832215 Factor a perfect square on the left side: (x + -0.1904761905)(x + -0.1904761905) = 1.17913832215 Calculate the square root of the right side: 1.085881357 Break this problem into two subproblems by setting (x + -0.1904761905) equal to 1.085881357 and -1.085881357.Subproblem 1
x + -0.1904761905 = 1.085881357 Simplifying x + -0.1904761905 = 1.085881357 Reorder the terms: -0.1904761905 + x = 1.085881357 Solving -0.1904761905 + x = 1.085881357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1904761905' to each side of the equation. -0.1904761905 + 0.1904761905 + x = 1.085881357 + 0.1904761905 Combine like terms: -0.1904761905 + 0.1904761905 = 0.0000000000 0.0000000000 + x = 1.085881357 + 0.1904761905 x = 1.085881357 + 0.1904761905 Combine like terms: 1.085881357 + 0.1904761905 = 1.2763575475 x = 1.2763575475 Simplifying x = 1.2763575475Subproblem 2
x + -0.1904761905 = -1.085881357 Simplifying x + -0.1904761905 = -1.085881357 Reorder the terms: -0.1904761905 + x = -1.085881357 Solving -0.1904761905 + x = -1.085881357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1904761905' to each side of the equation. -0.1904761905 + 0.1904761905 + x = -1.085881357 + 0.1904761905 Combine like terms: -0.1904761905 + 0.1904761905 = 0.0000000000 0.0000000000 + x = -1.085881357 + 0.1904761905 x = -1.085881357 + 0.1904761905 Combine like terms: -1.085881357 + 0.1904761905 = -0.8954051665 x = -0.8954051665 Simplifying x = -0.8954051665Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2763575475, -0.8954051665}
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