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Simplifying 4.9x2 + 48x + 10 = 0 Reorder the terms: 10 + 48x + 4.9x2 = 0 Solving 10 + 48x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 2.040816327 + 9.795918367x + x2 = 0 Move the constant term to the right: Add '-2.040816327' to each side of the equation. 2.040816327 + 9.795918367x + -2.040816327 + x2 = 0 + -2.040816327 Reorder the terms: 2.040816327 + -2.040816327 + 9.795918367x + x2 = 0 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + 9.795918367x + x2 = 0 + -2.040816327 9.795918367x + x2 = 0 + -2.040816327 Combine like terms: 0 + -2.040816327 = -2.040816327 9.795918367x + x2 = -2.040816327 The x term is 9.795918367x. Take half its coefficient (4.897959184). Square it (23.99000417) and add it to both sides. Add '23.99000417' to each side of the equation. 9.795918367x + 23.99000417 + x2 = -2.040816327 + 23.99000417 Reorder the terms: 23.99000417 + 9.795918367x + x2 = -2.040816327 + 23.99000417 Combine like terms: -2.040816327 + 23.99000417 = 21.949187843 23.99000417 + 9.795918367x + x2 = 21.949187843 Factor a perfect square on the left side: (x + 4.897959184)(x + 4.897959184) = 21.949187843 Calculate the square root of the right side: 4.684996034 Break this problem into two subproblems by setting (x + 4.897959184) equal to 4.684996034 and -4.684996034.Subproblem 1
x + 4.897959184 = 4.684996034 Simplifying x + 4.897959184 = 4.684996034 Reorder the terms: 4.897959184 + x = 4.684996034 Solving 4.897959184 + x = 4.684996034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.897959184' to each side of the equation. 4.897959184 + -4.897959184 + x = 4.684996034 + -4.897959184 Combine like terms: 4.897959184 + -4.897959184 = 0.000000000 0.000000000 + x = 4.684996034 + -4.897959184 x = 4.684996034 + -4.897959184 Combine like terms: 4.684996034 + -4.897959184 = -0.21296315 x = -0.21296315 Simplifying x = -0.21296315Subproblem 2
x + 4.897959184 = -4.684996034 Simplifying x + 4.897959184 = -4.684996034 Reorder the terms: 4.897959184 + x = -4.684996034 Solving 4.897959184 + x = -4.684996034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.897959184' to each side of the equation. 4.897959184 + -4.897959184 + x = -4.684996034 + -4.897959184 Combine like terms: 4.897959184 + -4.897959184 = 0.000000000 0.000000000 + x = -4.684996034 + -4.897959184 x = -4.684996034 + -4.897959184 Combine like terms: -4.684996034 + -4.897959184 = -9.582955218 x = -9.582955218 Simplifying x = -9.582955218Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.21296315, -9.582955218}
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