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Simplifying 8.01x2 + 3.19x = 5.81 Reorder the terms: 3.19x + 8.01x2 = 5.81 Solving 3.19x + 8.01x2 = 5.81 Solving for variable 'x'. Reorder the terms: -5.81 + 3.19x + 8.01x2 = 5.81 + -5.81 Combine like terms: 5.81 + -5.81 = 0.00 -5.81 + 3.19x + 8.01x2 = 0.00 Begin completing the square. Divide all terms by 8.01 the coefficient of the squared term: Divide each side by '8.01'. -0.7253433208 + 0.3982521848x + x2 = 0 Move the constant term to the right: Add '0.7253433208' to each side of the equation. -0.7253433208 + 0.3982521848x + 0.7253433208 + x2 = 0 + 0.7253433208 Reorder the terms: -0.7253433208 + 0.7253433208 + 0.3982521848x + x2 = 0 + 0.7253433208 Combine like terms: -0.7253433208 + 0.7253433208 = 0.0000000000 0.0000000000 + 0.3982521848x + x2 = 0 + 0.7253433208 0.3982521848x + x2 = 0 + 0.7253433208 Combine like terms: 0 + 0.7253433208 = 0.7253433208 0.3982521848x + x2 = 0.7253433208 The x term is 0.3982521848x. Take half its coefficient (0.1991260924). Square it (0.03965120067) and add it to both sides. Add '0.03965120067' to each side of the equation. 0.3982521848x + 0.03965120067 + x2 = 0.7253433208 + 0.03965120067 Reorder the terms: 0.03965120067 + 0.3982521848x + x2 = 0.7253433208 + 0.03965120067 Combine like terms: 0.7253433208 + 0.03965120067 = 0.76499452147 0.03965120067 + 0.3982521848x + x2 = 0.76499452147 Factor a perfect square on the left side: (x + 0.1991260924)(x + 0.1991260924) = 0.76499452147 Calculate the square root of the right side: 0.874639652 Break this problem into two subproblems by setting (x + 0.1991260924) equal to 0.874639652 and -0.874639652.Subproblem 1
x + 0.1991260924 = 0.874639652 Simplifying x + 0.1991260924 = 0.874639652 Reorder the terms: 0.1991260924 + x = 0.874639652 Solving 0.1991260924 + x = 0.874639652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1991260924' to each side of the equation. 0.1991260924 + -0.1991260924 + x = 0.874639652 + -0.1991260924 Combine like terms: 0.1991260924 + -0.1991260924 = 0.0000000000 0.0000000000 + x = 0.874639652 + -0.1991260924 x = 0.874639652 + -0.1991260924 Combine like terms: 0.874639652 + -0.1991260924 = 0.6755135596 x = 0.6755135596 Simplifying x = 0.6755135596Subproblem 2
x + 0.1991260924 = -0.874639652 Simplifying x + 0.1991260924 = -0.874639652 Reorder the terms: 0.1991260924 + x = -0.874639652 Solving 0.1991260924 + x = -0.874639652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1991260924' to each side of the equation. 0.1991260924 + -0.1991260924 + x = -0.874639652 + -0.1991260924 Combine like terms: 0.1991260924 + -0.1991260924 = 0.0000000000 0.0000000000 + x = -0.874639652 + -0.1991260924 x = -0.874639652 + -0.1991260924 Combine like terms: -0.874639652 + -0.1991260924 = -1.0737657444 x = -1.0737657444 Simplifying x = -1.0737657444Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6755135596, -1.0737657444}
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