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Simplifying (5x2 + -6x + -65) + (9x2 + 8) = 0 Reorder the terms: (-65 + -6x + 5x2) + (9x2 + 8) = 0 Remove parenthesis around (-65 + -6x + 5x2) -65 + -6x + 5x2 + (9x2 + 8) = 0 Reorder the terms: -65 + -6x + 5x2 + (8 + 9x2) = 0 Remove parenthesis around (8 + 9x2) -65 + -6x + 5x2 + 8 + 9x2 = 0 Reorder the terms: -65 + 8 + -6x + 5x2 + 9x2 = 0 Combine like terms: -65 + 8 = -57 -57 + -6x + 5x2 + 9x2 = 0 Combine like terms: 5x2 + 9x2 = 14x2 -57 + -6x + 14x2 = 0 Solving -57 + -6x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -4.071428571 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '4.071428571' to each side of the equation. -4.071428571 + -0.4285714286x + 4.071428571 + x2 = 0 + 4.071428571 Reorder the terms: -4.071428571 + 4.071428571 + -0.4285714286x + x2 = 0 + 4.071428571 Combine like terms: -4.071428571 + 4.071428571 = 0.000000000 0.000000000 + -0.4285714286x + x2 = 0 + 4.071428571 -0.4285714286x + x2 = 0 + 4.071428571 Combine like terms: 0 + 4.071428571 = 4.071428571 -0.4285714286x + x2 = 4.071428571 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = 4.071428571 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 4.071428571 + 0.04591836735 Combine like terms: 4.071428571 + 0.04591836735 = 4.11734693835 0.04591836735 + -0.4285714286x + x2 = 4.11734693835 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 4.11734693835 Calculate the square root of the right side: 2.029124673 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 2.029124673 and -2.029124673.Subproblem 1
x + -0.2142857143 = 2.029124673 Simplifying x + -0.2142857143 = 2.029124673 Reorder the terms: -0.2142857143 + x = 2.029124673 Solving -0.2142857143 + x = 2.029124673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 2.029124673 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 2.029124673 + 0.2142857143 x = 2.029124673 + 0.2142857143 Combine like terms: 2.029124673 + 0.2142857143 = 2.2434103873 x = 2.2434103873 Simplifying x = 2.2434103873Subproblem 2
x + -0.2142857143 = -2.029124673 Simplifying x + -0.2142857143 = -2.029124673 Reorder the terms: -0.2142857143 + x = -2.029124673 Solving -0.2142857143 + x = -2.029124673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -2.029124673 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -2.029124673 + 0.2142857143 x = -2.029124673 + 0.2142857143 Combine like terms: -2.029124673 + 0.2142857143 = -1.8148389587 x = -1.8148389587 Simplifying x = -1.8148389587Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2434103873, -1.8148389587}
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