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Simplifying -4.9x2 + 160x + 10 = 0 Reorder the terms: 10 + 160x + -4.9x2 = 0 Solving 10 + 160x + -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 + -32.65306122x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -32.65306122x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -32.65306122x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -32.65306122x + x2 = 0 + 2.040816327 -32.65306122x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -32.65306122x + x2 = 2.040816327 The x term is -32.65306122x. Take half its coefficient (-16.32653061). Square it (266.5556018) and add it to both sides. Add '266.5556018' to each side of the equation. -32.65306122x + 266.5556018 + x2 = 2.040816327 + 266.5556018 Reorder the terms: 266.5556018 + -32.65306122x + x2 = 2.040816327 + 266.5556018 Combine like terms: 2.040816327 + 266.5556018 = 268.596418127 266.5556018 + -32.65306122x + x2 = 268.596418127 Factor a perfect square on the left side: (x + -16.32653061)(x + -16.32653061) = 268.596418127 Calculate the square root of the right side: 16.388911438 Break this problem into two subproblems by setting (x + -16.32653061) equal to 16.388911438 and -16.388911438.Subproblem 1
x + -16.32653061 = 16.388911438 Simplifying x + -16.32653061 = 16.388911438 Reorder the terms: -16.32653061 + x = 16.388911438 Solving -16.32653061 + x = 16.388911438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.32653061' to each side of the equation. -16.32653061 + 16.32653061 + x = 16.388911438 + 16.32653061 Combine like terms: -16.32653061 + 16.32653061 = 0.00000000 0.00000000 + x = 16.388911438 + 16.32653061 x = 16.388911438 + 16.32653061 Combine like terms: 16.388911438 + 16.32653061 = 32.715442048 x = 32.715442048 Simplifying x = 32.715442048Subproblem 2
x + -16.32653061 = -16.388911438 Simplifying x + -16.32653061 = -16.388911438 Reorder the terms: -16.32653061 + x = -16.388911438 Solving -16.32653061 + x = -16.388911438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.32653061' to each side of the equation. -16.32653061 + 16.32653061 + x = -16.388911438 + 16.32653061 Combine like terms: -16.32653061 + 16.32653061 = 0.00000000 0.00000000 + x = -16.388911438 + 16.32653061 x = -16.388911438 + 16.32653061 Combine like terms: -16.388911438 + 16.32653061 = -0.062380828 x = -0.062380828 Simplifying x = -0.062380828Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.715442048, -0.062380828}
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