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Simplifying 3x + -3x2 + -18 = -40 Reorder the terms: -18 + 3x + -3x2 = -40 Solving -18 + 3x + -3x2 = -40 Solving for variable 'x'. Reorder the terms: -18 + 40 + 3x + -3x2 = -40 + 40 Combine like terms: -18 + 40 = 22 22 + 3x + -3x2 = -40 + 40 Combine like terms: -40 + 40 = 0 22 + 3x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -7.333333333 + -1x + x2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + -1x + 7.333333333 + x2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + -1x + x2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + -1x + x2 = 0 + 7.333333333 -1x + x2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 -1x + x2 = 7.333333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 7.333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 7.333333333 + 0.25 Combine like terms: 7.333333333 + 0.25 = 7.583333333 0.25 + -1x + x2 = 7.583333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 7.583333333 Calculate the square root of the right side: 2.753785274 Break this problem into two subproblems by setting (x + -0.5) equal to 2.753785274 and -2.753785274.Subproblem 1
x + -0.5 = 2.753785274 Simplifying x + -0.5 = 2.753785274 Reorder the terms: -0.5 + x = 2.753785274 Solving -0.5 + x = 2.753785274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.753785274 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.753785274 + 0.5 x = 2.753785274 + 0.5 Combine like terms: 2.753785274 + 0.5 = 3.253785274 x = 3.253785274 Simplifying x = 3.253785274Subproblem 2
x + -0.5 = -2.753785274 Simplifying x + -0.5 = -2.753785274 Reorder the terms: -0.5 + x = -2.753785274 Solving -0.5 + x = -2.753785274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.753785274 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.753785274 + 0.5 x = -2.753785274 + 0.5 Combine like terms: -2.753785274 + 0.5 = -2.253785274 x = -2.253785274 Simplifying x = -2.253785274Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.253785274, -2.253785274}
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