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Simplifying 0 = (0.5) + -9.81x2 + 3x + 1.8 0 = 0.5 + -9.81x2 + 3x + 1.8 Reorder the terms: 0 = 0.5 + 1.8 + 3x + -9.81x2 Combine like terms: 0.5 + 1.8 = 2.3 0 = 2.3 + 3x + -9.81x2 Solving 0 = 2.3 + 3x + -9.81x2 Solving for variable 'x'. Combine like terms: 0 + -2.3 = -2.3 -2.3 + -3x + 9.81x2 = 2.3 + 3x + -9.81x2 + -2.3 + -3x + 9.81x2 Reorder the terms: -2.3 + -3x + 9.81x2 = 2.3 + -2.3 + 3x + -3x + -9.81x2 + 9.81x2 Combine like terms: 2.3 + -2.3 = 0.0 -2.3 + -3x + 9.81x2 = 0.0 + 3x + -3x + -9.81x2 + 9.81x2 -2.3 + -3x + 9.81x2 = 3x + -3x + -9.81x2 + 9.81x2 Combine like terms: 3x + -3x = 0 -2.3 + -3x + 9.81x2 = 0 + -9.81x2 + 9.81x2 -2.3 + -3x + 9.81x2 = -9.81x2 + 9.81x2 Combine like terms: -9.81x2 + 9.81x2 = 0.00 -2.3 + -3x + 9.81x2 = 0.00 Begin completing the square. Divide all terms by 9.81 the coefficient of the squared term: Divide each side by '9.81'. -0.2344546381 + -0.3058103976x + x2 = 0 Move the constant term to the right: Add '0.2344546381' to each side of the equation. -0.2344546381 + -0.3058103976x + 0.2344546381 + x2 = 0 + 0.2344546381 Reorder the terms: -0.2344546381 + 0.2344546381 + -0.3058103976x + x2 = 0 + 0.2344546381 Combine like terms: -0.2344546381 + 0.2344546381 = 0.0000000000 0.0000000000 + -0.3058103976x + x2 = 0 + 0.2344546381 -0.3058103976x + x2 = 0 + 0.2344546381 Combine like terms: 0 + 0.2344546381 = 0.2344546381 -0.3058103976x + x2 = 0.2344546381 The x term is -0.3058103976x. Take half its coefficient (-0.1529051988). Square it (0.02337999982) and add it to both sides. Add '0.02337999982' to each side of the equation. -0.3058103976x + 0.02337999982 + x2 = 0.2344546381 + 0.02337999982 Reorder the terms: 0.02337999982 + -0.3058103976x + x2 = 0.2344546381 + 0.02337999982 Combine like terms: 0.2344546381 + 0.02337999982 = 0.25783463792 0.02337999982 + -0.3058103976x + x2 = 0.25783463792 Factor a perfect square on the left side: (x + -0.1529051988)(x + -0.1529051988) = 0.25783463792 Calculate the square root of the right side: 0.5077742 Break this problem into two subproblems by setting (x + -0.1529051988) equal to 0.5077742 and -0.5077742.Subproblem 1
x + -0.1529051988 = 0.5077742 Simplifying x + -0.1529051988 = 0.5077742 Reorder the terms: -0.1529051988 + x = 0.5077742 Solving -0.1529051988 + x = 0.5077742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1529051988' to each side of the equation. -0.1529051988 + 0.1529051988 + x = 0.5077742 + 0.1529051988 Combine like terms: -0.1529051988 + 0.1529051988 = 0.0000000000 0.0000000000 + x = 0.5077742 + 0.1529051988 x = 0.5077742 + 0.1529051988 Combine like terms: 0.5077742 + 0.1529051988 = 0.6606793988 x = 0.6606793988 Simplifying x = 0.6606793988Subproblem 2
x + -0.1529051988 = -0.5077742 Simplifying x + -0.1529051988 = -0.5077742 Reorder the terms: -0.1529051988 + x = -0.5077742 Solving -0.1529051988 + x = -0.5077742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1529051988' to each side of the equation. -0.1529051988 + 0.1529051988 + x = -0.5077742 + 0.1529051988 Combine like terms: -0.1529051988 + 0.1529051988 = 0.0000000000 0.0000000000 + x = -0.5077742 + 0.1529051988 x = -0.5077742 + 0.1529051988 Combine like terms: -0.5077742 + 0.1529051988 = -0.3548690012 x = -0.3548690012 Simplifying x = -0.3548690012Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6606793988, -0.3548690012}
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