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Simplifying 0 = 4.9x2 + -4x + -5 Reorder the terms: 0 = -5 + -4x + 4.9x2 Solving 0 = -5 + -4x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + 4x + -4.9x2 = -5 + -4x + 4.9x2 + 5 + 4x + -4.9x2 Reorder the terms: 5 + 4x + -4.9x2 = -5 + 5 + -4x + 4x + 4.9x2 + -4.9x2 Combine like terms: -5 + 5 = 0 5 + 4x + -4.9x2 = 0 + -4x + 4x + 4.9x2 + -4.9x2 5 + 4x + -4.9x2 = -4x + 4x + 4.9x2 + -4.9x2 Combine like terms: -4x + 4x = 0 5 + 4x + -4.9x2 = 0 + 4.9x2 + -4.9x2 5 + 4x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 5 + 4x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -1.020408163 + -0.8163265306x + x2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + -0.8163265306x + 1.020408163 + x2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + -0.8163265306x + x2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + -0.8163265306x + x2 = 0 + 1.020408163 -0.8163265306x + x2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 -0.8163265306x + x2 = 1.020408163 The x term is -0.8163265306x. Take half its coefficient (-0.4081632653). Square it (0.1665972511) and add it to both sides. Add '0.1665972511' to each side of the equation. -0.8163265306x + 0.1665972511 + x2 = 1.020408163 + 0.1665972511 Reorder the terms: 0.1665972511 + -0.8163265306x + x2 = 1.020408163 + 0.1665972511 Combine like terms: 1.020408163 + 0.1665972511 = 1.1870054141 0.1665972511 + -0.8163265306x + x2 = 1.1870054141 Factor a perfect square on the left side: (x + -0.4081632653)(x + -0.4081632653) = 1.1870054141 Calculate the square root of the right side: 1.089497781 Break this problem into two subproblems by setting (x + -0.4081632653) equal to 1.089497781 and -1.089497781.Subproblem 1
x + -0.4081632653 = 1.089497781 Simplifying x + -0.4081632653 = 1.089497781 Reorder the terms: -0.4081632653 + x = 1.089497781 Solving -0.4081632653 + x = 1.089497781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.4081632653 + x = 1.089497781 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + x = 1.089497781 + 0.4081632653 x = 1.089497781 + 0.4081632653 Combine like terms: 1.089497781 + 0.4081632653 = 1.4976610463 x = 1.4976610463 Simplifying x = 1.4976610463Subproblem 2
x + -0.4081632653 = -1.089497781 Simplifying x + -0.4081632653 = -1.089497781 Reorder the terms: -0.4081632653 + x = -1.089497781 Solving -0.4081632653 + x = -1.089497781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.4081632653 + x = -1.089497781 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + x = -1.089497781 + 0.4081632653 x = -1.089497781 + 0.4081632653 Combine like terms: -1.089497781 + 0.4081632653 = -0.6813345157 x = -0.6813345157 Simplifying x = -0.6813345157Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4976610463, -0.6813345157}
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