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Simplifying 0 = 0.21x2 + -0.4x + -1.6 Reorder the terms: 0 = -1.6 + -0.4x + 0.21x2 Solving 0 = -1.6 + -0.4x + 0.21x2 Solving for variable 'x'. Combine like terms: 0 + 1.6 = 1.6 1.6 + 0.4x + -0.21x2 = -1.6 + -0.4x + 0.21x2 + 1.6 + 0.4x + -0.21x2 Reorder the terms: 1.6 + 0.4x + -0.21x2 = -1.6 + 1.6 + -0.4x + 0.4x + 0.21x2 + -0.21x2 Combine like terms: -1.6 + 1.6 = 0.0 1.6 + 0.4x + -0.21x2 = 0.0 + -0.4x + 0.4x + 0.21x2 + -0.21x2 1.6 + 0.4x + -0.21x2 = -0.4x + 0.4x + 0.21x2 + -0.21x2 Combine like terms: -0.4x + 0.4x = 0.0 1.6 + 0.4x + -0.21x2 = 0.0 + 0.21x2 + -0.21x2 1.6 + 0.4x + -0.21x2 = 0.21x2 + -0.21x2 Combine like terms: 0.21x2 + -0.21x2 = 0.00 1.6 + 0.4x + -0.21x2 = 0.00 Begin completing the square. Divide all terms by -0.21 the coefficient of the squared term: Divide each side by '-0.21'. -7.619047619 + -1.904761905x + x2 = 0 Move the constant term to the right: Add '7.619047619' to each side of the equation. -7.619047619 + -1.904761905x + 7.619047619 + x2 = 0 + 7.619047619 Reorder the terms: -7.619047619 + 7.619047619 + -1.904761905x + x2 = 0 + 7.619047619 Combine like terms: -7.619047619 + 7.619047619 = 0.000000000 0.000000000 + -1.904761905x + x2 = 0 + 7.619047619 -1.904761905x + x2 = 0 + 7.619047619 Combine like terms: 0 + 7.619047619 = 7.619047619 -1.904761905x + x2 = 7.619047619 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 = 7.619047619 + 0.9070294787 Reorder the terms: 0.9070294787 + -1.904761905x + x2 = 7.619047619 + 0.9070294787 Combine like terms: 7.619047619 + 0.9070294787 = 8.5260770977 0.9070294787 + -1.904761905x + x2 = 8.5260770977 Factor a perfect square on the left side: (x + -0.9523809525)(x + -0.9523809525) = 8.5260770977 Calculate the square root of the right side: 2.919944708 Break this problem into two subproblems by setting (x + -0.9523809525) equal to 2.919944708 and -2.919944708.Subproblem 1
x + -0.9523809525 = 2.919944708 Simplifying x + -0.9523809525 = 2.919944708 Reorder the terms: -0.9523809525 + x = 2.919944708 Solving -0.9523809525 + x = 2.919944708 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 = 2.919944708 + 0.9523809525 Combine like terms: -0.9523809525 + 0.9523809525 = 0.0000000000 0.0000000000 + x = 2.919944708 + 0.9523809525 x = 2.919944708 + 0.9523809525 Combine like terms: 2.919944708 + 0.9523809525 = 3.8723256605 x = 3.8723256605 Simplifying x = 3.8723256605Subproblem 2
x + -0.9523809525 = -2.919944708 Simplifying x + -0.9523809525 = -2.919944708 Reorder the terms: -0.9523809525 + x = -2.919944708 Solving -0.9523809525 + x = -2.919944708 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 = -2.919944708 + 0.9523809525 Combine like terms: -0.9523809525 + 0.9523809525 = 0.0000000000 0.0000000000 + x = -2.919944708 + 0.9523809525 x = -2.919944708 + 0.9523809525 Combine like terms: -2.919944708 + 0.9523809525 = -1.9675637555 x = -1.9675637555 Simplifying x = -1.9675637555Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.8723256605, -1.9675637555}
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