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Simplifying 21x2 + -4x + -40 = 0 Reorder the terms: -40 + -4x + 21x2 = 0 Solving -40 + -4x + 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'. -1.904761905 + -0.1904761905x + x2 = 0 Move the constant term to the right: Add '1.904761905' to each side of the equation. -1.904761905 + -0.1904761905x + 1.904761905 + x2 = 0 + 1.904761905 Reorder the terms: -1.904761905 + 1.904761905 + -0.1904761905x + x2 = 0 + 1.904761905 Combine like terms: -1.904761905 + 1.904761905 = 0.000000000 0.000000000 + -0.1904761905x + x2 = 0 + 1.904761905 -0.1904761905x + x2 = 0 + 1.904761905 Combine like terms: 0 + 1.904761905 = 1.904761905 -0.1904761905x + x2 = 1.904761905 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 = 1.904761905 + 0.009070294787 Reorder the terms: 0.009070294787 + -0.1904761905x + x2 = 1.904761905 + 0.009070294787 Combine like terms: 1.904761905 + 0.009070294787 = 1.913832199787 0.009070294787 + -0.1904761905x + x2 = 1.913832199787 Factor a perfect square on the left side: (x + -0.09523809525)(x + -0.09523809525) = 1.913832199787 Calculate the square root of the right side: 1.383413243 Break this problem into two subproblems by setting (x + -0.09523809525) equal to 1.383413243 and -1.383413243.Subproblem 1
x + -0.09523809525 = 1.383413243 Simplifying x + -0.09523809525 = 1.383413243 Reorder the terms: -0.09523809525 + x = 1.383413243 Solving -0.09523809525 + x = 1.383413243 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 = 1.383413243 + 0.09523809525 Combine like terms: -0.09523809525 + 0.09523809525 = 0.00000000000 0.00000000000 + x = 1.383413243 + 0.09523809525 x = 1.383413243 + 0.09523809525 Combine like terms: 1.383413243 + 0.09523809525 = 1.47865133825 x = 1.47865133825 Simplifying x = 1.47865133825Subproblem 2
x + -0.09523809525 = -1.383413243 Simplifying x + -0.09523809525 = -1.383413243 Reorder the terms: -0.09523809525 + x = -1.383413243 Solving -0.09523809525 + x = -1.383413243 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 = -1.383413243 + 0.09523809525 Combine like terms: -0.09523809525 + 0.09523809525 = 0.00000000000 0.00000000000 + x = -1.383413243 + 0.09523809525 x = -1.383413243 + 0.09523809525 Combine like terms: -1.383413243 + 0.09523809525 = -1.28817514775 x = -1.28817514775 Simplifying x = -1.28817514775Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.47865133825, -1.28817514775}
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