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Simplifying 4x + 3x2 + -1x + 2 = 30 Reorder the terms: 2 + 4x + -1x + 3x2 = 30 Combine like terms: 4x + -1x = 3x 2 + 3x + 3x2 = 30 Solving 2 + 3x + 3x2 = 30 Solving for variable 'x'. Reorder the terms: 2 + -30 + 3x + 3x2 = 30 + -30 Combine like terms: 2 + -30 = -28 -28 + 3x + 3x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -28 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.333333333 + x + x2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + x + 9.333333333 + x2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + x + x2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + x + x2 = 0 + 9.333333333 x + x2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 x + x2 = 9.333333333 The x term is x. 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. + 0.25 + x2 = 9.333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 9.333333333 + 0.25 Combine like terms: 9.333333333 + 0.25 = 9.583333333 1.25 + x2 = 9.583333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 9.583333333 Calculate the square root of the right side: 3.095695937 Break this problem into two subproblems by setting (x + 0.5) equal to 3.095695937 and -3.095695937.Subproblem 1
x + 0.5 = 3.095695937 Simplifying x + 0.5 = 3.095695937 Reorder the terms: 0.5 + x = 3.095695937 Solving 0.5 + x = 3.095695937 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 = 3.095695937 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.095695937 + -0.5 x = 3.095695937 + -0.5 Combine like terms: 3.095695937 + -0.5 = 2.595695937 x = 2.595695937 Simplifying x = 2.595695937Subproblem 2
x + 0.5 = -3.095695937 Simplifying x + 0.5 = -3.095695937 Reorder the terms: 0.5 + x = -3.095695937 Solving 0.5 + x = -3.095695937 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 = -3.095695937 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.095695937 + -0.5 x = -3.095695937 + -0.5 Combine like terms: -3.095695937 + -0.5 = -3.595695937 x = -3.595695937 Simplifying x = -3.595695937Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.595695937, -3.595695937}
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