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Simplifying -4.2X2 + -0.2X + 5.3 = 0 Reorder the terms: 5.3 + -0.2X + -4.2X2 = 0 Solving 5.3 + -0.2X + -4.2X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -4.2 the coefficient of the squared term: Divide each side by '-4.2'. -1.261904762 + 0.04761904762X + X2 = 0 Move the constant term to the right: Add '1.261904762' to each side of the equation. -1.261904762 + 0.04761904762X + 1.261904762 + X2 = 0 + 1.261904762 Reorder the terms: -1.261904762 + 1.261904762 + 0.04761904762X + X2 = 0 + 1.261904762 Combine like terms: -1.261904762 + 1.261904762 = 0.000000000 0.000000000 + 0.04761904762X + X2 = 0 + 1.261904762 0.04761904762X + X2 = 0 + 1.261904762 Combine like terms: 0 + 1.261904762 = 1.261904762 0.04761904762X + X2 = 1.261904762 The X term is 0.04761904762X. Take half its coefficient (0.02380952381). Square it (0.0005668934241) and add it to both sides. Add '0.0005668934241' to each side of the equation. 0.04761904762X + 0.0005668934241 + X2 = 1.261904762 + 0.0005668934241 Reorder the terms: 0.0005668934241 + 0.04761904762X + X2 = 1.261904762 + 0.0005668934241 Combine like terms: 1.261904762 + 0.0005668934241 = 1.2624716554241 0.0005668934241 + 0.04761904762X + X2 = 1.2624716554241 Factor a perfect square on the left side: (X + 0.02380952381)(X + 0.02380952381) = 1.2624716554241 Calculate the square root of the right side: 1.123597639 Break this problem into two subproblems by setting (X + 0.02380952381) equal to 1.123597639 and -1.123597639.Subproblem 1
X + 0.02380952381 = 1.123597639 Simplifying X + 0.02380952381 = 1.123597639 Reorder the terms: 0.02380952381 + X = 1.123597639 Solving 0.02380952381 + X = 1.123597639 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.02380952381' to each side of the equation. 0.02380952381 + -0.02380952381 + X = 1.123597639 + -0.02380952381 Combine like terms: 0.02380952381 + -0.02380952381 = 0.00000000000 0.00000000000 + X = 1.123597639 + -0.02380952381 X = 1.123597639 + -0.02380952381 Combine like terms: 1.123597639 + -0.02380952381 = 1.09978811519 X = 1.09978811519 Simplifying X = 1.09978811519Subproblem 2
X + 0.02380952381 = -1.123597639 Simplifying X + 0.02380952381 = -1.123597639 Reorder the terms: 0.02380952381 + X = -1.123597639 Solving 0.02380952381 + X = -1.123597639 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.02380952381' to each side of the equation. 0.02380952381 + -0.02380952381 + X = -1.123597639 + -0.02380952381 Combine like terms: 0.02380952381 + -0.02380952381 = 0.00000000000 0.00000000000 + X = -1.123597639 + -0.02380952381 X = -1.123597639 + -0.02380952381 Combine like terms: -1.123597639 + -0.02380952381 = -1.14740716281 X = -1.14740716281 Simplifying X = -1.14740716281Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.09978811519, -1.14740716281}
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