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Simplifying (9x2 + -3x + -30) + (4x2 + 7x) = 0 Reorder the terms: (-30 + -3x + 9x2) + (4x2 + 7x) = 0 Remove parenthesis around (-30 + -3x + 9x2) -30 + -3x + 9x2 + (4x2 + 7x) = 0 Reorder the terms: -30 + -3x + 9x2 + (7x + 4x2) = 0 Remove parenthesis around (7x + 4x2) -30 + -3x + 9x2 + 7x + 4x2 = 0 Reorder the terms: -30 + -3x + 7x + 9x2 + 4x2 = 0 Combine like terms: -3x + 7x = 4x -30 + 4x + 9x2 + 4x2 = 0 Combine like terms: 9x2 + 4x2 = 13x2 -30 + 4x + 13x2 = 0 Solving -30 + 4x + 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'. -2.307692308 + 0.3076923077x + x2 = 0 Move the constant term to the right: Add '2.307692308' to each side of the equation. -2.307692308 + 0.3076923077x + 2.307692308 + x2 = 0 + 2.307692308 Reorder the terms: -2.307692308 + 2.307692308 + 0.3076923077x + x2 = 0 + 2.307692308 Combine like terms: -2.307692308 + 2.307692308 = 0.000000000 0.000000000 + 0.3076923077x + x2 = 0 + 2.307692308 0.3076923077x + x2 = 0 + 2.307692308 Combine like terms: 0 + 2.307692308 = 2.307692308 0.3076923077x + x2 = 2.307692308 The x term is 0.3076923077x. Take half its coefficient (0.1538461539). Square it (0.02366863907) and add it to both sides. Add '0.02366863907' to each side of the equation. 0.3076923077x + 0.02366863907 + x2 = 2.307692308 + 0.02366863907 Reorder the terms: 0.02366863907 + 0.3076923077x + x2 = 2.307692308 + 0.02366863907 Combine like terms: 2.307692308 + 0.02366863907 = 2.33136094707 0.02366863907 + 0.3076923077x + x2 = 2.33136094707 Factor a perfect square on the left side: (x + 0.1538461539)(x + 0.1538461539) = 2.33136094707 Calculate the square root of the right side: 1.52687948 Break this problem into two subproblems by setting (x + 0.1538461539) equal to 1.52687948 and -1.52687948.Subproblem 1
x + 0.1538461539 = 1.52687948 Simplifying x + 0.1538461539 = 1.52687948 Reorder the terms: 0.1538461539 + x = 1.52687948 Solving 0.1538461539 + x = 1.52687948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1538461539' to each side of the equation. 0.1538461539 + -0.1538461539 + x = 1.52687948 + -0.1538461539 Combine like terms: 0.1538461539 + -0.1538461539 = 0.0000000000 0.0000000000 + x = 1.52687948 + -0.1538461539 x = 1.52687948 + -0.1538461539 Combine like terms: 1.52687948 + -0.1538461539 = 1.3730333261 x = 1.3730333261 Simplifying x = 1.3730333261Subproblem 2
x + 0.1538461539 = -1.52687948 Simplifying x + 0.1538461539 = -1.52687948 Reorder the terms: 0.1538461539 + x = -1.52687948 Solving 0.1538461539 + x = -1.52687948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1538461539' to each side of the equation. 0.1538461539 + -0.1538461539 + x = -1.52687948 + -0.1538461539 Combine like terms: 0.1538461539 + -0.1538461539 = 0.0000000000 0.0000000000 + x = -1.52687948 + -0.1538461539 x = -1.52687948 + -0.1538461539 Combine like terms: -1.52687948 + -0.1538461539 = -1.6807256339 x = -1.6807256339 Simplifying x = -1.6807256339Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3730333261, -1.6807256339}
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