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Simplifying x + 4 + 3 + x + -2 + x2 + 2x + 3x + -4 = 30 Reorder the terms: 4 + 3 + -2 + -4 + x + x + 2x + 3x + x2 = 30 Combine like terms: 4 + 3 = 7 7 + -2 + -4 + x + x + 2x + 3x + x2 = 30 Combine like terms: 7 + -2 = 5 5 + -4 + x + x + 2x + 3x + x2 = 30 Combine like terms: 5 + -4 = 1 1 + x + x + 2x + 3x + x2 = 30 Combine like terms: x + x = 2x 1 + 2x + 2x + 3x + x2 = 30 Combine like terms: 2x + 2x = 4x 1 + 4x + 3x + x2 = 30 Combine like terms: 4x + 3x = 7x 1 + 7x + x2 = 30 Solving 1 + 7x + x2 = 30 Solving for variable 'x'. Reorder the terms: 1 + -30 + 7x + x2 = 30 + -30 Combine like terms: 1 + -30 = -29 -29 + 7x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -29 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 7x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 7x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 7x + x2 = 0 + 29 7x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 7x + x2 = 29 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 29 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 29 + 12.25 Combine like terms: 29 + 12.25 = 41.25 12.25 + 7x + x2 = 41.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + 3.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + 3.5 = 6.422616289 Simplifying x + 3.5 = 6.422616289 Reorder the terms: 3.5 + x = 6.422616289 Solving 3.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.422616289 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.422616289 + -3.5 x = 6.422616289 + -3.5 Combine like terms: 6.422616289 + -3.5 = 2.922616289 x = 2.922616289 Simplifying x = 2.922616289Subproblem 2
x + 3.5 = -6.422616289 Simplifying x + 3.5 = -6.422616289 Reorder the terms: 3.5 + x = -6.422616289 Solving 3.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.422616289 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.422616289 + -3.5 x = -6.422616289 + -3.5 Combine like terms: -6.422616289 + -3.5 = -9.922616289 x = -9.922616289 Simplifying x = -9.922616289Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.922616289, -9.922616289}
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