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Simplifying 49x2 + 48x + -4 = 0 Reorder the terms: -4 + 48x + 49x2 = 0 Solving -4 + 48x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.08163265306 + 0.9795918367x + x2 = 0 Move the constant term to the right: Add '0.08163265306' to each side of the equation. -0.08163265306 + 0.9795918367x + 0.08163265306 + x2 = 0 + 0.08163265306 Reorder the terms: -0.08163265306 + 0.08163265306 + 0.9795918367x + x2 = 0 + 0.08163265306 Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000 0.00000000000 + 0.9795918367x + x2 = 0 + 0.08163265306 0.9795918367x + x2 = 0 + 0.08163265306 Combine like terms: 0 + 0.08163265306 = 0.08163265306 0.9795918367x + x2 = 0.08163265306 The x term is 0.9795918367x. Take half its coefficient (0.4897959184). Square it (0.2399000417) and add it to both sides. Add '0.2399000417' to each side of the equation. 0.9795918367x + 0.2399000417 + x2 = 0.08163265306 + 0.2399000417 Reorder the terms: 0.2399000417 + 0.9795918367x + x2 = 0.08163265306 + 0.2399000417 Combine like terms: 0.08163265306 + 0.2399000417 = 0.32153269476 0.2399000417 + 0.9795918367x + x2 = 0.32153269476 Factor a perfect square on the left side: (x + 0.4897959184)(x + 0.4897959184) = 0.32153269476 Calculate the square root of the right side: 0.56703853 Break this problem into two subproblems by setting (x + 0.4897959184) equal to 0.56703853 and -0.56703853.Subproblem 1
x + 0.4897959184 = 0.56703853 Simplifying x + 0.4897959184 = 0.56703853 Reorder the terms: 0.4897959184 + x = 0.56703853 Solving 0.4897959184 + x = 0.56703853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4897959184' to each side of the equation. 0.4897959184 + -0.4897959184 + x = 0.56703853 + -0.4897959184 Combine like terms: 0.4897959184 + -0.4897959184 = 0.0000000000 0.0000000000 + x = 0.56703853 + -0.4897959184 x = 0.56703853 + -0.4897959184 Combine like terms: 0.56703853 + -0.4897959184 = 0.0772426116 x = 0.0772426116 Simplifying x = 0.0772426116Subproblem 2
x + 0.4897959184 = -0.56703853 Simplifying x + 0.4897959184 = -0.56703853 Reorder the terms: 0.4897959184 + x = -0.56703853 Solving 0.4897959184 + x = -0.56703853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4897959184' to each side of the equation. 0.4897959184 + -0.4897959184 + x = -0.56703853 + -0.4897959184 Combine like terms: 0.4897959184 + -0.4897959184 = 0.0000000000 0.0000000000 + x = -0.56703853 + -0.4897959184 x = -0.56703853 + -0.4897959184 Combine like terms: -0.56703853 + -0.4897959184 = -1.0568344484 x = -1.0568344484 Simplifying x = -1.0568344484Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0772426116, -1.0568344484}
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