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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 = -34x -34x + 21x2 = -1 Solving -34x + 21x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + -34x + 21x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -34x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.04761904762 + -1.619047619x + x2 = 0 Move the constant term to the right: Add '-0.04761904762' to each side of the equation. 0.04761904762 + -1.619047619x + -0.04761904762 + x2 = 0 + -0.04761904762 Reorder the terms: 0.04761904762 + -0.04761904762 + -1.619047619x + x2 = 0 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + -1.619047619x + x2 = 0 + -0.04761904762 -1.619047619x + x2 = 0 + -0.04761904762 Combine like terms: 0 + -0.04761904762 = -0.04761904762 -1.619047619x + x2 = -0.04761904762 The x term is -1.619047619x. Take half its coefficient (-0.8095238095). Square it (0.6553287981) and add it to both sides. Add '0.6553287981' to each side of the equation. -1.619047619x + 0.6553287981 + x2 = -0.04761904762 + 0.6553287981 Reorder the terms: 0.6553287981 + -1.619047619x + x2 = -0.04761904762 + 0.6553287981 Combine like terms: -0.04761904762 + 0.6553287981 = 0.60770975048 0.6553287981 + -1.619047619x + x2 = 0.60770975048 Factor a perfect square on the left side: (x + -0.8095238095)(x + -0.8095238095) = 0.60770975048 Calculate the square root of the right side: 0.779557407 Break this problem into two subproblems by setting (x + -0.8095238095) equal to 0.779557407 and -0.779557407.Subproblem 1
x + -0.8095238095 = 0.779557407 Simplifying x + -0.8095238095 = 0.779557407 Reorder the terms: -0.8095238095 + x = 0.779557407 Solving -0.8095238095 + x = 0.779557407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8095238095' to each side of the equation. -0.8095238095 + 0.8095238095 + x = 0.779557407 + 0.8095238095 Combine like terms: -0.8095238095 + 0.8095238095 = 0.0000000000 0.0000000000 + x = 0.779557407 + 0.8095238095 x = 0.779557407 + 0.8095238095 Combine like terms: 0.779557407 + 0.8095238095 = 1.5890812165 x = 1.5890812165 Simplifying x = 1.5890812165Subproblem 2
x + -0.8095238095 = -0.779557407 Simplifying x + -0.8095238095 = -0.779557407 Reorder the terms: -0.8095238095 + x = -0.779557407 Solving -0.8095238095 + x = -0.779557407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8095238095' to each side of the equation. -0.8095238095 + 0.8095238095 + x = -0.779557407 + 0.8095238095 Combine like terms: -0.8095238095 + 0.8095238095 = 0.0000000000 0.0000000000 + x = -0.779557407 + 0.8095238095 x = -0.779557407 + 0.8095238095 Combine like terms: -0.779557407 + 0.8095238095 = 0.0299664025 x = 0.0299664025 Simplifying x = 0.0299664025Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5890812165, 0.0299664025}
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