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Simplifying 63x2 + -30x = 3 Reorder the terms: -30x + 63x2 = 3 Solving -30x + 63x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -30x + 63x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -30x + 63x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -10x + 21x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -10x + 21x2)' equal to zero and attempt to solve: Simplifying -1 + -10x + 21x2 = 0 Solving -1 + -10x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.04761904762 + -0.4761904762x + x2 = 0 Move the constant term to the right: Add '0.04761904762' to each side of the equation. -0.04761904762 + -0.4761904762x + 0.04761904762 + x2 = 0 + 0.04761904762 Reorder the terms: -0.04761904762 + 0.04761904762 + -0.4761904762x + x2 = 0 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + -0.4761904762x + x2 = 0 + 0.04761904762 -0.4761904762x + x2 = 0 + 0.04761904762 Combine like terms: 0 + 0.04761904762 = 0.04761904762 -0.4761904762x + x2 = 0.04761904762 The x term is -0.4761904762x. Take half its coefficient (-0.2380952381). Square it (0.05668934241) and add it to both sides. Add '0.05668934241' to each side of the equation. -0.4761904762x + 0.05668934241 + x2 = 0.04761904762 + 0.05668934241 Reorder the terms: 0.05668934241 + -0.4761904762x + x2 = 0.04761904762 + 0.05668934241 Combine like terms: 0.04761904762 + 0.05668934241 = 0.10430839003 0.05668934241 + -0.4761904762x + x2 = 0.10430839003 Factor a perfect square on the left side: (x + -0.2380952381)(x + -0.2380952381) = 0.10430839003 Calculate the square root of the right side: 0.322968094 Break this problem into two subproblems by setting (x + -0.2380952381) equal to 0.322968094 and -0.322968094.Subproblem 1
x + -0.2380952381 = 0.322968094 Simplifying x + -0.2380952381 = 0.322968094 Reorder the terms: -0.2380952381 + x = 0.322968094 Solving -0.2380952381 + x = 0.322968094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2380952381' to each side of the equation. -0.2380952381 + 0.2380952381 + x = 0.322968094 + 0.2380952381 Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000 0.0000000000 + x = 0.322968094 + 0.2380952381 x = 0.322968094 + 0.2380952381 Combine like terms: 0.322968094 + 0.2380952381 = 0.5610633321 x = 0.5610633321 Simplifying x = 0.5610633321Subproblem 2
x + -0.2380952381 = -0.322968094 Simplifying x + -0.2380952381 = -0.322968094 Reorder the terms: -0.2380952381 + x = -0.322968094 Solving -0.2380952381 + x = -0.322968094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2380952381' to each side of the equation. -0.2380952381 + 0.2380952381 + x = -0.322968094 + 0.2380952381 Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000 0.0000000000 + x = -0.322968094 + 0.2380952381 x = -0.322968094 + 0.2380952381 Combine like terms: -0.322968094 + 0.2380952381 = -0.0848728559 x = -0.0848728559 Simplifying x = -0.0848728559Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5610633321, -0.0848728559}Solution
x = {0.5610633321, -0.0848728559}
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