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Simplifying (11x + 19) + -1(7x2 + 9x + 3) = 1.41421356237 Reorder the terms: (19 + 11x) + -1(7x2 + 9x + 3) = 1.41421356237 Remove parenthesis around (19 + 11x) 19 + 11x + -1(7x2 + 9x + 3) = 1.41421356237 Reorder the terms: 19 + 11x + -1(3 + 9x + 7x2) = 1.41421356237 19 + 11x + (3 * -1 + 9x * -1 + 7x2 * -1) = 1.41421356237 19 + 11x + (-3 + -9x + -7x2) = 1.41421356237 Reorder the terms: 19 + -3 + 11x + -9x + -7x2 = 1.41421356237 Combine like terms: 19 + -3 = 16 16 + 11x + -9x + -7x2 = 1.41421356237 Combine like terms: 11x + -9x = 2x 16 + 2x + -7x2 = 1.41421356237 Solving 16 + 2x + -7x2 = 1.41421356237 Solving for variable 'x'. Reorder the terms: 16 + -1.41421356237 + 2x + -7x2 = 1.41421356237 + -1.41421356237 Combine like terms: 16 + -1.41421356237 = 14.58578643763 14.58578643763 + 2x + -7x2 = 1.41421356237 + -1.41421356237 Combine like terms: 1.41421356237 + -1.41421356237 = 0.00000000000 14.58578643763 + 2x + -7x2 = 0.00000000000 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -2.083683777 + -0.2857142857x + x2 = 0.00000000000 Move the constant term to the right: Add '2.083683777' to each side of the equation. -2.083683777 + -0.2857142857x + 2.083683777 + x2 = 0.00000000000 + 2.083683777 Reorder the terms: -2.083683777 + 2.083683777 + -0.2857142857x + x2 = 0.00000000000 + 2.083683777 Combine like terms: -2.083683777 + 2.083683777 = 0.000000000 0.000000000 + -0.2857142857x + x2 = 0.00000000000 + 2.083683777 -0.2857142857x + x2 = 0.00000000000 + 2.083683777 Combine like terms: 0.00000000000 + 2.083683777 = 2.083683777 -0.2857142857x + x2 = 2.083683777 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 = 2.083683777 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 2.083683777 + 0.02040816328 Combine like terms: 2.083683777 + 0.02040816328 = 2.10409194028 0.02040816328 + -0.2857142857x + x2 = 2.10409194028 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 2.10409194028 Calculate the square root of the right side: 1.450548841 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 1.450548841 and -1.450548841.Subproblem 1
x + -0.1428571429 = 1.450548841 Simplifying x + -0.1428571429 = 1.450548841 Reorder the terms: -0.1428571429 + x = 1.450548841 Solving -0.1428571429 + x = 1.450548841 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 = 1.450548841 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.450548841 + 0.1428571429 x = 1.450548841 + 0.1428571429 Combine like terms: 1.450548841 + 0.1428571429 = 1.5934059839 x = 1.5934059839 Simplifying x = 1.5934059839Subproblem 2
x + -0.1428571429 = -1.450548841 Simplifying x + -0.1428571429 = -1.450548841 Reorder the terms: -0.1428571429 + x = -1.450548841 Solving -0.1428571429 + x = -1.450548841 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 = -1.450548841 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.450548841 + 0.1428571429 x = -1.450548841 + 0.1428571429 Combine like terms: -1.450548841 + 0.1428571429 = -1.3076916981 x = -1.3076916981 Simplifying x = -1.3076916981Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5934059839, -1.3076916981}
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