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Simplifying (11x + 19) = (7x2 + 9x + 3) Reorder the terms: (19 + 11x) = (7x2 + 9x + 3) Remove parenthesis around (19 + 11x) 19 + 11x = (7x2 + 9x + 3) Reorder the terms: 19 + 11x = (3 + 9x + 7x2) Remove parenthesis around (3 + 9x + 7x2) 19 + 11x = 3 + 9x + 7x2 Solving 19 + 11x = 3 + 9x + 7x2 Solving for variable 'x'. Reorder the terms: 19 + -3 + 11x + -9x + -7x2 = 3 + 9x + 7x2 + -3 + -9x + -7x2 Combine like terms: 19 + -3 = 16 16 + 11x + -9x + -7x2 = 3 + 9x + 7x2 + -3 + -9x + -7x2 Combine like terms: 11x + -9x = 2x 16 + 2x + -7x2 = 3 + 9x + 7x2 + -3 + -9x + -7x2 Reorder the terms: 16 + 2x + -7x2 = 3 + -3 + 9x + -9x + 7x2 + -7x2 Combine like terms: 3 + -3 = 0 16 + 2x + -7x2 = 0 + 9x + -9x + 7x2 + -7x2 16 + 2x + -7x2 = 9x + -9x + 7x2 + -7x2 Combine like terms: 9x + -9x = 0 16 + 2x + -7x2 = 0 + 7x2 + -7x2 16 + 2x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 16 + 2x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -2.285714286 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + -0.2857142857x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + -0.2857142857x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + -0.2857142857x + x2 = 0 + 2.285714286 -0.2857142857x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 -0.2857142857x + x2 = 2.285714286 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 2.285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 2.285714286 + 0.02040816328 Combine like terms: 2.285714286 + 0.02040816328 = 2.30612244928 0.02040816328 + -0.2857142857x + x2 = 2.30612244928 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 2.30612244928 Calculate the square root of the right side: 1.518592259 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 1.518592259 and -1.518592259.Subproblem 1
x + -0.1428571429 = 1.518592259 Simplifying x + -0.1428571429 = 1.518592259 Reorder the terms: -0.1428571429 + x = 1.518592259 Solving -0.1428571429 + x = 1.518592259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 1.518592259 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.518592259 + 0.1428571429 x = 1.518592259 + 0.1428571429 Combine like terms: 1.518592259 + 0.1428571429 = 1.6614494019 x = 1.6614494019 Simplifying x = 1.6614494019Subproblem 2
x + -0.1428571429 = -1.518592259 Simplifying x + -0.1428571429 = -1.518592259 Reorder the terms: -0.1428571429 + x = -1.518592259 Solving -0.1428571429 + x = -1.518592259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -1.518592259 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.518592259 + 0.1428571429 x = -1.518592259 + 0.1428571429 Combine like terms: -1.518592259 + 0.1428571429 = -1.3757351161 x = -1.3757351161 Simplifying x = -1.3757351161Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6614494019, -1.3757351161}
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