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Simplifying 7x + -3(9 + -7x) * x = -1 Reorder the terms for easier multiplication: 7x + -3x(9 + -7x) = -1 7x + (9 * -3x + -7x * -3x) = -1 7x + (-27x + 21x2) = -1 Combine like terms: 7x + -27x = -20x -20x + 21x2 = -1 Solving -20x + 21x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + -20x + 21x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -20x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.04761904762 + -0.9523809524x + x2 = 0 Move the constant term to the right: Add '-0.04761904762' to each side of the equation. 0.04761904762 + -0.9523809524x + -0.04761904762 + x2 = 0 + -0.04761904762 Reorder the terms: 0.04761904762 + -0.04761904762 + -0.9523809524x + x2 = 0 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + -0.9523809524x + x2 = 0 + -0.04761904762 -0.9523809524x + x2 = 0 + -0.04761904762 Combine like terms: 0 + -0.04761904762 = -0.04761904762 -0.9523809524x + x2 = -0.04761904762 The x term is -0.9523809524x. Take half its coefficient (-0.4761904762). Square it (0.2267573696) and add it to both sides. Add '0.2267573696' to each side of the equation. -0.9523809524x + 0.2267573696 + x2 = -0.04761904762 + 0.2267573696 Reorder the terms: 0.2267573696 + -0.9523809524x + x2 = -0.04761904762 + 0.2267573696 Combine like terms: -0.04761904762 + 0.2267573696 = 0.17913832198 0.2267573696 + -0.9523809524x + x2 = 0.17913832198 Factor a perfect square on the left side: (x + -0.4761904762)(x + -0.4761904762) = 0.17913832198 Calculate the square root of the right side: 0.423247353 Break this problem into two subproblems by setting (x + -0.4761904762) equal to 0.423247353 and -0.423247353.Subproblem 1
x + -0.4761904762 = 0.423247353 Simplifying x + -0.4761904762 = 0.423247353 Reorder the terms: -0.4761904762 + x = 0.423247353 Solving -0.4761904762 + x = 0.423247353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4761904762' to each side of the equation. -0.4761904762 + 0.4761904762 + x = 0.423247353 + 0.4761904762 Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000 0.0000000000 + x = 0.423247353 + 0.4761904762 x = 0.423247353 + 0.4761904762 Combine like terms: 0.423247353 + 0.4761904762 = 0.8994378292 x = 0.8994378292 Simplifying x = 0.8994378292Subproblem 2
x + -0.4761904762 = -0.423247353 Simplifying x + -0.4761904762 = -0.423247353 Reorder the terms: -0.4761904762 + x = -0.423247353 Solving -0.4761904762 + x = -0.423247353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4761904762' to each side of the equation. -0.4761904762 + 0.4761904762 + x = -0.423247353 + 0.4761904762 Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000 0.0000000000 + x = -0.423247353 + 0.4761904762 x = -0.423247353 + 0.4761904762 Combine like terms: -0.423247353 + 0.4761904762 = 0.0529431232 x = 0.0529431232 Simplifying x = 0.0529431232Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8994378292, 0.0529431232}
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