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Simplifying 21x2 + 2x = 17 Reorder the terms: 2x + 21x2 = 17 Solving 2x + 21x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + 2x + 21x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 2x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.8095238095 + 0.09523809524x + x2 = 0 Move the constant term to the right: Add '0.8095238095' to each side of the equation. -0.8095238095 + 0.09523809524x + 0.8095238095 + x2 = 0 + 0.8095238095 Reorder the terms: -0.8095238095 + 0.8095238095 + 0.09523809524x + x2 = 0 + 0.8095238095 Combine like terms: -0.8095238095 + 0.8095238095 = 0.0000000000 0.0000000000 + 0.09523809524x + x2 = 0 + 0.8095238095 0.09523809524x + x2 = 0 + 0.8095238095 Combine like terms: 0 + 0.8095238095 = 0.8095238095 0.09523809524x + x2 = 0.8095238095 The x term is 0.09523809524x. Take half its coefficient (0.04761904762). Square it (0.002267573696) and add it to both sides. Add '0.002267573696' to each side of the equation. 0.09523809524x + 0.002267573696 + x2 = 0.8095238095 + 0.002267573696 Reorder the terms: 0.002267573696 + 0.09523809524x + x2 = 0.8095238095 + 0.002267573696 Combine like terms: 0.8095238095 + 0.002267573696 = 0.811791383196 0.002267573696 + 0.09523809524x + x2 = 0.811791383196 Factor a perfect square on the left side: (x + 0.04761904762)(x + 0.04761904762) = 0.811791383196 Calculate the square root of the right side: 0.900994663 Break this problem into two subproblems by setting (x + 0.04761904762) equal to 0.900994663 and -0.900994663.Subproblem 1
x + 0.04761904762 = 0.900994663 Simplifying x + 0.04761904762 = 0.900994663 Reorder the terms: 0.04761904762 + x = 0.900994663 Solving 0.04761904762 + x = 0.900994663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04761904762' to each side of the equation. 0.04761904762 + -0.04761904762 + x = 0.900994663 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + x = 0.900994663 + -0.04761904762 x = 0.900994663 + -0.04761904762 Combine like terms: 0.900994663 + -0.04761904762 = 0.85337561538 x = 0.85337561538 Simplifying x = 0.85337561538Subproblem 2
x + 0.04761904762 = -0.900994663 Simplifying x + 0.04761904762 = -0.900994663 Reorder the terms: 0.04761904762 + x = -0.900994663 Solving 0.04761904762 + x = -0.900994663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04761904762' to each side of the equation. 0.04761904762 + -0.04761904762 + x = -0.900994663 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + x = -0.900994663 + -0.04761904762 x = -0.900994663 + -0.04761904762 Combine like terms: -0.900994663 + -0.04761904762 = -0.94861371062 x = -0.94861371062 Simplifying x = -0.94861371062Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.85337561538, -0.94861371062}
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