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Simplifying (6x2 + -7x + 21) + (8x2 + 9x + -72) = 0 Reorder the terms: (21 + -7x + 6x2) + (8x2 + 9x + -72) = 0 Remove parenthesis around (21 + -7x + 6x2) 21 + -7x + 6x2 + (8x2 + 9x + -72) = 0 Reorder the terms: 21 + -7x + 6x2 + (-72 + 9x + 8x2) = 0 Remove parenthesis around (-72 + 9x + 8x2) 21 + -7x + 6x2 + -72 + 9x + 8x2 = 0 Reorder the terms: 21 + -72 + -7x + 9x + 6x2 + 8x2 = 0 Combine like terms: 21 + -72 = -51 -51 + -7x + 9x + 6x2 + 8x2 = 0 Combine like terms: -7x + 9x = 2x -51 + 2x + 6x2 + 8x2 = 0 Combine like terms: 6x2 + 8x2 = 14x2 -51 + 2x + 14x2 = 0 Solving -51 + 2x + 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'. -3.642857143 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '3.642857143' to each side of the equation. -3.642857143 + 0.1428571429x + 3.642857143 + x2 = 0 + 3.642857143 Reorder the terms: -3.642857143 + 3.642857143 + 0.1428571429x + x2 = 0 + 3.642857143 Combine like terms: -3.642857143 + 3.642857143 = 0.000000000 0.000000000 + 0.1428571429x + x2 = 0 + 3.642857143 0.1428571429x + x2 = 0 + 3.642857143 Combine like terms: 0 + 3.642857143 = 3.642857143 0.1428571429x + x2 = 3.642857143 The x term is 0.1428571429x. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429x + 0.005102040819 + x2 = 3.642857143 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 3.642857143 + 0.005102040819 Combine like terms: 3.642857143 + 0.005102040819 = 3.647959183819 0.005102040819 + 0.1428571429x + x2 = 3.647959183819 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 3.647959183819 Calculate the square root of the right side: 1.909963137 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 1.909963137 and -1.909963137.Subproblem 1
x + 0.07142857145 = 1.909963137 Simplifying x + 0.07142857145 = 1.909963137 Reorder the terms: 0.07142857145 + x = 1.909963137 Solving 0.07142857145 + x = 1.909963137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = 1.909963137 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 1.909963137 + -0.07142857145 x = 1.909963137 + -0.07142857145 Combine like terms: 1.909963137 + -0.07142857145 = 1.83853456555 x = 1.83853456555 Simplifying x = 1.83853456555Subproblem 2
x + 0.07142857145 = -1.909963137 Simplifying x + 0.07142857145 = -1.909963137 Reorder the terms: 0.07142857145 + x = -1.909963137 Solving 0.07142857145 + x = -1.909963137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = -1.909963137 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -1.909963137 + -0.07142857145 x = -1.909963137 + -0.07142857145 Combine like terms: -1.909963137 + -0.07142857145 = -1.98139170845 x = -1.98139170845 Simplifying x = -1.98139170845Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.83853456555, -1.98139170845}
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