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Simplifying 42x2 + -482x + -2459 = 0 Reorder the terms: -2459 + -482x + 42x2 = 0 Solving -2459 + -482x + 42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -58.54761905 + -11.47619048x + x2 = 0 Move the constant term to the right: Add '58.54761905' to each side of the equation. -58.54761905 + -11.47619048x + 58.54761905 + x2 = 0 + 58.54761905 Reorder the terms: -58.54761905 + 58.54761905 + -11.47619048x + x2 = 0 + 58.54761905 Combine like terms: -58.54761905 + 58.54761905 = 0.00000000 0.00000000 + -11.47619048x + x2 = 0 + 58.54761905 -11.47619048x + x2 = 0 + 58.54761905 Combine like terms: 0 + 58.54761905 = 58.54761905 -11.47619048x + x2 = 58.54761905 The x term is -11.47619048x. Take half its coefficient (-5.73809524). Square it (32.92573698) and add it to both sides. Add '32.92573698' to each side of the equation. -11.47619048x + 32.92573698 + x2 = 58.54761905 + 32.92573698 Reorder the terms: 32.92573698 + -11.47619048x + x2 = 58.54761905 + 32.92573698 Combine like terms: 58.54761905 + 32.92573698 = 91.47335603 32.92573698 + -11.47619048x + x2 = 91.47335603 Factor a perfect square on the left side: (x + -5.73809524)(x + -5.73809524) = 91.47335603 Calculate the square root of the right side: 9.564170431 Break this problem into two subproblems by setting (x + -5.73809524) equal to 9.564170431 and -9.564170431.Subproblem 1
x + -5.73809524 = 9.564170431 Simplifying x + -5.73809524 = 9.564170431 Reorder the terms: -5.73809524 + x = 9.564170431 Solving -5.73809524 + x = 9.564170431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.73809524' to each side of the equation. -5.73809524 + 5.73809524 + x = 9.564170431 + 5.73809524 Combine like terms: -5.73809524 + 5.73809524 = 0.00000000 0.00000000 + x = 9.564170431 + 5.73809524 x = 9.564170431 + 5.73809524 Combine like terms: 9.564170431 + 5.73809524 = 15.302265671 x = 15.302265671 Simplifying x = 15.302265671Subproblem 2
x + -5.73809524 = -9.564170431 Simplifying x + -5.73809524 = -9.564170431 Reorder the terms: -5.73809524 + x = -9.564170431 Solving -5.73809524 + x = -9.564170431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.73809524' to each side of the equation. -5.73809524 + 5.73809524 + x = -9.564170431 + 5.73809524 Combine like terms: -5.73809524 + 5.73809524 = 0.00000000 0.00000000 + x = -9.564170431 + 5.73809524 x = -9.564170431 + 5.73809524 Combine like terms: -9.564170431 + 5.73809524 = -3.826075191 x = -3.826075191 Simplifying x = -3.826075191Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.302265671, -3.826075191}
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