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Simplifying 3.39x2 + -4.6x + 15 = 44 Reorder the terms: 15 + -4.6x + 3.39x2 = 44 Solving 15 + -4.6x + 3.39x2 = 44 Solving for variable 'x'. Reorder the terms: 15 + -44 + -4.6x + 3.39x2 = 44 + -44 Combine like terms: 15 + -44 = -29 -29 + -4.6x + 3.39x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -29 + -4.6x + 3.39x2 = 0 Begin completing the square. Divide all terms by 3.39 the coefficient of the squared term: Divide each side by '3.39'. -8.554572271 + -1.356932153x + x2 = 0 Move the constant term to the right: Add '8.554572271' to each side of the equation. -8.554572271 + -1.356932153x + 8.554572271 + x2 = 0 + 8.554572271 Reorder the terms: -8.554572271 + 8.554572271 + -1.356932153x + x2 = 0 + 8.554572271 Combine like terms: -8.554572271 + 8.554572271 = 0.000000000 0.000000000 + -1.356932153x + x2 = 0 + 8.554572271 -1.356932153x + x2 = 0 + 8.554572271 Combine like terms: 0 + 8.554572271 = 8.554572271 -1.356932153x + x2 = 8.554572271 The x term is -1.356932153x. Take half its coefficient (-0.6784660765). Square it (0.4603162170) and add it to both sides. Add '0.4603162170' to each side of the equation. -1.356932153x + 0.4603162170 + x2 = 8.554572271 + 0.4603162170 Reorder the terms: 0.4603162170 + -1.356932153x + x2 = 8.554572271 + 0.4603162170 Combine like terms: 8.554572271 + 0.4603162170 = 9.014888488 0.4603162170 + -1.356932153x + x2 = 9.014888488 Factor a perfect square on the left side: (x + -0.6784660765)(x + -0.6784660765) = 9.014888488 Calculate the square root of the right side: 3.002480389 Break this problem into two subproblems by setting (x + -0.6784660765) equal to 3.002480389 and -3.002480389.Subproblem 1
x + -0.6784660765 = 3.002480389 Simplifying x + -0.6784660765 = 3.002480389 Reorder the terms: -0.6784660765 + x = 3.002480389 Solving -0.6784660765 + x = 3.002480389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6784660765' to each side of the equation. -0.6784660765 + 0.6784660765 + x = 3.002480389 + 0.6784660765 Combine like terms: -0.6784660765 + 0.6784660765 = 0.0000000000 0.0000000000 + x = 3.002480389 + 0.6784660765 x = 3.002480389 + 0.6784660765 Combine like terms: 3.002480389 + 0.6784660765 = 3.6809464655 x = 3.6809464655 Simplifying x = 3.6809464655Subproblem 2
x + -0.6784660765 = -3.002480389 Simplifying x + -0.6784660765 = -3.002480389 Reorder the terms: -0.6784660765 + x = -3.002480389 Solving -0.6784660765 + x = -3.002480389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6784660765' to each side of the equation. -0.6784660765 + 0.6784660765 + x = -3.002480389 + 0.6784660765 Combine like terms: -0.6784660765 + 0.6784660765 = 0.0000000000 0.0000000000 + x = -3.002480389 + 0.6784660765 x = -3.002480389 + 0.6784660765 Combine like terms: -3.002480389 + 0.6784660765 = -2.3240143125 x = -2.3240143125 Simplifying x = -2.3240143125Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6809464655, -2.3240143125}
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