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Simplifying 4.6(x2 + -3x + 2) = x2 Reorder the terms: 4.6(2 + -3x + x2) = x2 (2 * 4.6 + -3x * 4.6 + x2 * 4.6) = x2 (9.2 + -13.8x + 4.6x2) = x2 Solving 9.2 + -13.8x + 4.6x2 = x2 Solving for variable 'x'. Combine like terms: 4.6x2 + -1x2 = 3.6x2 9.2 + -13.8x + 3.6x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 9.2 + -13.8x + 3.6x2 = 0 Begin completing the square. Divide all terms by 3.6 the coefficient of the squared term: Divide each side by '3.6'. 2.555555556 + -3.833333333x + x2 = 0 Move the constant term to the right: Add '-2.555555556' to each side of the equation. 2.555555556 + -3.833333333x + -2.555555556 + x2 = 0 + -2.555555556 Reorder the terms: 2.555555556 + -2.555555556 + -3.833333333x + x2 = 0 + -2.555555556 Combine like terms: 2.555555556 + -2.555555556 = 0.000000000 0.000000000 + -3.833333333x + x2 = 0 + -2.555555556 -3.833333333x + x2 = 0 + -2.555555556 Combine like terms: 0 + -2.555555556 = -2.555555556 -3.833333333x + x2 = -2.555555556 The x term is -3.833333333x. Take half its coefficient (-1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. -3.833333333x + 3.673611112 + x2 = -2.555555556 + 3.673611112 Reorder the terms: 3.673611112 + -3.833333333x + x2 = -2.555555556 + 3.673611112 Combine like terms: -2.555555556 + 3.673611112 = 1.118055556 3.673611112 + -3.833333333x + x2 = 1.118055556 Factor a perfect square on the left side: (x + -1.916666667)(x + -1.916666667) = 1.118055556 Calculate the square root of the right side: 1.057381462 Break this problem into two subproblems by setting (x + -1.916666667) equal to 1.057381462 and -1.057381462.Subproblem 1
x + -1.916666667 = 1.057381462 Simplifying x + -1.916666667 = 1.057381462 Reorder the terms: -1.916666667 + x = 1.057381462 Solving -1.916666667 + x = 1.057381462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = 1.057381462 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = 1.057381462 + 1.916666667 x = 1.057381462 + 1.916666667 Combine like terms: 1.057381462 + 1.916666667 = 2.974048129 x = 2.974048129 Simplifying x = 2.974048129Subproblem 2
x + -1.916666667 = -1.057381462 Simplifying x + -1.916666667 = -1.057381462 Reorder the terms: -1.916666667 + x = -1.057381462 Solving -1.916666667 + x = -1.057381462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = -1.057381462 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = -1.057381462 + 1.916666667 x = -1.057381462 + 1.916666667 Combine like terms: -1.057381462 + 1.916666667 = 0.859285205 x = 0.859285205 Simplifying x = 0.859285205Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.974048129, 0.859285205}
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