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Simplifying 21x2 + -40x + -128 = 0 Reorder the terms: -128 + -40x + 21x2 = 0 Solving -128 + -40x + 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'. -6.095238095 + -1.904761905x + x2 = 0 Move the constant term to the right: Add '6.095238095' to each side of the equation. -6.095238095 + -1.904761905x + 6.095238095 + x2 = 0 + 6.095238095 Reorder the terms: -6.095238095 + 6.095238095 + -1.904761905x + x2 = 0 + 6.095238095 Combine like terms: -6.095238095 + 6.095238095 = 0.000000000 0.000000000 + -1.904761905x + x2 = 0 + 6.095238095 -1.904761905x + x2 = 0 + 6.095238095 Combine like terms: 0 + 6.095238095 = 6.095238095 -1.904761905x + x2 = 6.095238095 The x term is -1.904761905x. Take half its coefficient (-0.9523809525). Square it (0.9070294787) and add it to both sides. Add '0.9070294787' to each side of the equation. -1.904761905x + 0.9070294787 + x2 = 6.095238095 + 0.9070294787 Reorder the terms: 0.9070294787 + -1.904761905x + x2 = 6.095238095 + 0.9070294787 Combine like terms: 6.095238095 + 0.9070294787 = 7.0022675737 0.9070294787 + -1.904761905x + x2 = 7.0022675737 Factor a perfect square on the left side: (x + -0.9523809525)(x + -0.9523809525) = 7.0022675737 Calculate the square root of the right side: 2.646179808 Break this problem into two subproblems by setting (x + -0.9523809525) equal to 2.646179808 and -2.646179808.Subproblem 1
x + -0.9523809525 = 2.646179808 Simplifying x + -0.9523809525 = 2.646179808 Reorder the terms: -0.9523809525 + x = 2.646179808 Solving -0.9523809525 + x = 2.646179808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9523809525' to each side of the equation. -0.9523809525 + 0.9523809525 + x = 2.646179808 + 0.9523809525 Combine like terms: -0.9523809525 + 0.9523809525 = 0.0000000000 0.0000000000 + x = 2.646179808 + 0.9523809525 x = 2.646179808 + 0.9523809525 Combine like terms: 2.646179808 + 0.9523809525 = 3.5985607605 x = 3.5985607605 Simplifying x = 3.5985607605Subproblem 2
x + -0.9523809525 = -2.646179808 Simplifying x + -0.9523809525 = -2.646179808 Reorder the terms: -0.9523809525 + x = -2.646179808 Solving -0.9523809525 + x = -2.646179808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9523809525' to each side of the equation. -0.9523809525 + 0.9523809525 + x = -2.646179808 + 0.9523809525 Combine like terms: -0.9523809525 + 0.9523809525 = 0.0000000000 0.0000000000 + x = -2.646179808 + 0.9523809525 x = -2.646179808 + 0.9523809525 Combine like terms: -2.646179808 + 0.9523809525 = -1.6937988555 x = -1.6937988555 Simplifying x = -1.6937988555Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5985607605, -1.6937988555}
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