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Simplifying -21x2 + 20x + 32 = 0 Reorder the terms: 32 + 20x + -21x2 = 0 Solving 32 + 20x + -21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -1.523809524 + -0.9523809524x + x2 = 0 Move the constant term to the right: Add '1.523809524' to each side of the equation. -1.523809524 + -0.9523809524x + 1.523809524 + x2 = 0 + 1.523809524 Reorder the terms: -1.523809524 + 1.523809524 + -0.9523809524x + x2 = 0 + 1.523809524 Combine like terms: -1.523809524 + 1.523809524 = 0.000000000 0.000000000 + -0.9523809524x + x2 = 0 + 1.523809524 -0.9523809524x + x2 = 0 + 1.523809524 Combine like terms: 0 + 1.523809524 = 1.523809524 -0.9523809524x + x2 = 1.523809524 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 = 1.523809524 + 0.2267573696 Reorder the terms: 0.2267573696 + -0.9523809524x + x2 = 1.523809524 + 0.2267573696 Combine like terms: 1.523809524 + 0.2267573696 = 1.7505668936 0.2267573696 + -0.9523809524x + x2 = 1.7505668936 Factor a perfect square on the left side: (x + -0.4761904762)(x + -0.4761904762) = 1.7505668936 Calculate the square root of the right side: 1.323089904 Break this problem into two subproblems by setting (x + -0.4761904762) equal to 1.323089904 and -1.323089904.Subproblem 1
x + -0.4761904762 = 1.323089904 Simplifying x + -0.4761904762 = 1.323089904 Reorder the terms: -0.4761904762 + x = 1.323089904 Solving -0.4761904762 + x = 1.323089904 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 = 1.323089904 + 0.4761904762 Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000 0.0000000000 + x = 1.323089904 + 0.4761904762 x = 1.323089904 + 0.4761904762 Combine like terms: 1.323089904 + 0.4761904762 = 1.7992803802 x = 1.7992803802 Simplifying x = 1.7992803802Subproblem 2
x + -0.4761904762 = -1.323089904 Simplifying x + -0.4761904762 = -1.323089904 Reorder the terms: -0.4761904762 + x = -1.323089904 Solving -0.4761904762 + x = -1.323089904 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 = -1.323089904 + 0.4761904762 Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000 0.0000000000 + x = -1.323089904 + 0.4761904762 x = -1.323089904 + 0.4761904762 Combine like terms: -1.323089904 + 0.4761904762 = -0.8468994278 x = -0.8468994278 Simplifying x = -0.8468994278Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7992803802, -0.8468994278}
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