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Simplifying 286 = x(21x + -4) Reorder the terms: 286 = x(-4 + 21x) 286 = (-4 * x + 21x * x) 286 = (-4x + 21x2) Solving 286 = -4x + 21x2 Solving for variable 'x'. Reorder the terms: 286 + 4x + -21x2 = -4x + 4x + 21x2 + -21x2 Combine like terms: -4x + 4x = 0 286 + 4x + -21x2 = 0 + 21x2 + -21x2 286 + 4x + -21x2 = 21x2 + -21x2 Combine like terms: 21x2 + -21x2 = 0 286 + 4x + -21x2 = 0 Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -13.61904762 + -0.1904761905x + x2 = 0 Move the constant term to the right: Add '13.61904762' to each side of the equation. -13.61904762 + -0.1904761905x + 13.61904762 + x2 = 0 + 13.61904762 Reorder the terms: -13.61904762 + 13.61904762 + -0.1904761905x + x2 = 0 + 13.61904762 Combine like terms: -13.61904762 + 13.61904762 = 0.00000000 0.00000000 + -0.1904761905x + x2 = 0 + 13.61904762 -0.1904761905x + x2 = 0 + 13.61904762 Combine like terms: 0 + 13.61904762 = 13.61904762 -0.1904761905x + x2 = 13.61904762 The x term is -0.1904761905x. Take half its coefficient (-0.09523809525). Square it (0.009070294787) and add it to both sides. Add '0.009070294787' to each side of the equation. -0.1904761905x + 0.009070294787 + x2 = 13.61904762 + 0.009070294787 Reorder the terms: 0.009070294787 + -0.1904761905x + x2 = 13.61904762 + 0.009070294787 Combine like terms: 13.61904762 + 0.009070294787 = 13.628117914787 0.009070294787 + -0.1904761905x + x2 = 13.628117914787 Factor a perfect square on the left side: (x + -0.09523809525)(x + -0.09523809525) = 13.628117914787 Calculate the square root of the right side: 3.691628085 Break this problem into two subproblems by setting (x + -0.09523809525) equal to 3.691628085 and -3.691628085.Subproblem 1
x + -0.09523809525 = 3.691628085 Simplifying x + -0.09523809525 = 3.691628085 Reorder the terms: -0.09523809525 + x = 3.691628085 Solving -0.09523809525 + x = 3.691628085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09523809525' to each side of the equation. -0.09523809525 + 0.09523809525 + x = 3.691628085 + 0.09523809525 Combine like terms: -0.09523809525 + 0.09523809525 = 0.00000000000 0.00000000000 + x = 3.691628085 + 0.09523809525 x = 3.691628085 + 0.09523809525 Combine like terms: 3.691628085 + 0.09523809525 = 3.78686618025 x = 3.78686618025 Simplifying x = 3.78686618025Subproblem 2
x + -0.09523809525 = -3.691628085 Simplifying x + -0.09523809525 = -3.691628085 Reorder the terms: -0.09523809525 + x = -3.691628085 Solving -0.09523809525 + x = -3.691628085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09523809525' to each side of the equation. -0.09523809525 + 0.09523809525 + x = -3.691628085 + 0.09523809525 Combine like terms: -0.09523809525 + 0.09523809525 = 0.00000000000 0.00000000000 + x = -3.691628085 + 0.09523809525 x = -3.691628085 + 0.09523809525 Combine like terms: -3.691628085 + 0.09523809525 = -3.59638998975 x = -3.59638998975 Simplifying x = -3.59638998975Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.78686618025, -3.59638998975}
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