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Simplifying 3 = -0.6x2 + x + 4 Reorder the terms: 3 = 4 + x + -0.6x2 Solving 3 = 4 + x + -0.6x2 Solving for variable 'x'. Combine like terms: 3 + -4 = -1 -1 + -1x + 0.6x2 = 4 + x + -0.6x2 + -4 + -1x + 0.6x2 Reorder the terms: -1 + -1x + 0.6x2 = 4 + -4 + x + -1x + -0.6x2 + 0.6x2 Combine like terms: 4 + -4 = 0 -1 + -1x + 0.6x2 = 0 + x + -1x + -0.6x2 + 0.6x2 -1 + -1x + 0.6x2 = x + -1x + -0.6x2 + 0.6x2 Combine like terms: x + -1x = 0 -1 + -1x + 0.6x2 = 0 + -0.6x2 + 0.6x2 -1 + -1x + 0.6x2 = -0.6x2 + 0.6x2 Combine like terms: -0.6x2 + 0.6x2 = 0.0 -1 + -1x + 0.6x2 = 0.0 Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -1.666666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -1.666666667x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -1.666666667x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 1.666666667 -1.666666667x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -1.666666667x + x2 = 1.666666667 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 1.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 1.666666667 + 0.6944444447 Combine like terms: 1.666666667 + 0.6944444447 = 2.3611111117 0.6944444447 + -1.666666667x + x2 = 2.3611111117 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 2.3611111117 Calculate the square root of the right side: 1.536590743 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.536590743 and -1.536590743.Subproblem 1
x + -0.8333333335 = 1.536590743 Simplifying x + -0.8333333335 = 1.536590743 Reorder the terms: -0.8333333335 + x = 1.536590743 Solving -0.8333333335 + x = 1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.536590743 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.536590743 + 0.8333333335 x = 1.536590743 + 0.8333333335 Combine like terms: 1.536590743 + 0.8333333335 = 2.3699240765 x = 2.3699240765 Simplifying x = 2.3699240765Subproblem 2
x + -0.8333333335 = -1.536590743 Simplifying x + -0.8333333335 = -1.536590743 Reorder the terms: -0.8333333335 + x = -1.536590743 Solving -0.8333333335 + x = -1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.536590743 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.536590743 + 0.8333333335 x = -1.536590743 + 0.8333333335 Combine like terms: -1.536590743 + 0.8333333335 = -0.7032574095 x = -0.7032574095 Simplifying x = -0.7032574095Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3699240765, -0.7032574095}
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