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Simplifying -1.80 + -4.0x + 4.9(x2) = 0 Solving -1.80 + -4.0x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.3673469388 + -0.8163265306x + x2 = 0 Move the constant term to the right: Add '0.3673469388' to each side of the equation. -0.3673469388 + -0.8163265306x + 0.3673469388 + x2 = 0 + 0.3673469388 Reorder the terms: -0.3673469388 + 0.3673469388 + -0.8163265306x + x2 = 0 + 0.3673469388 Combine like terms: -0.3673469388 + 0.3673469388 = 0.0000000000 0.0000000000 + -0.8163265306x + x2 = 0 + 0.3673469388 -0.8163265306x + x2 = 0 + 0.3673469388 Combine like terms: 0 + 0.3673469388 = 0.3673469388 -0.8163265306x + x2 = 0.3673469388 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 = 0.3673469388 + 0.1665972511 Reorder the terms: 0.1665972511 + -0.8163265306x + x2 = 0.3673469388 + 0.1665972511 Combine like terms: 0.3673469388 + 0.1665972511 = 0.5339441899 0.1665972511 + -0.8163265306x + x2 = 0.5339441899 Factor a perfect square on the left side: (x + -0.4081632653)(x + -0.4081632653) = 0.5339441899 Calculate the square root of the right side: 0.730714849 Break this problem into two subproblems by setting (x + -0.4081632653) equal to 0.730714849 and -0.730714849.Subproblem 1
x + -0.4081632653 = 0.730714849 Simplifying x + -0.4081632653 = 0.730714849 Reorder the terms: -0.4081632653 + x = 0.730714849 Solving -0.4081632653 + x = 0.730714849 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 = 0.730714849 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + x = 0.730714849 + 0.4081632653 x = 0.730714849 + 0.4081632653 Combine like terms: 0.730714849 + 0.4081632653 = 1.1388781143 x = 1.1388781143 Simplifying x = 1.1388781143Subproblem 2
x + -0.4081632653 = -0.730714849 Simplifying x + -0.4081632653 = -0.730714849 Reorder the terms: -0.4081632653 + x = -0.730714849 Solving -0.4081632653 + x = -0.730714849 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 = -0.730714849 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + x = -0.730714849 + 0.4081632653 x = -0.730714849 + 0.4081632653 Combine like terms: -0.730714849 + 0.4081632653 = -0.3225515837 x = -0.3225515837 Simplifying x = -0.3225515837Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1388781143, -0.3225515837}
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