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Simplifying -4x2 + 29x + 30 = 0 Reorder the terms: 30 + 29x + -4x2 = 0 Solving 30 + 29x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -7.5 + -7.25x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -7.25x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -7.25x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -7.25x + x2 = 0 + 7.5 -7.25x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -7.25x + x2 = 7.5 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = 7.5 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = 7.5 + 13.140625 Combine like terms: 7.5 + 13.140625 = 20.640625 13.140625 + -7.25x + x2 = 20.640625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 20.640625 Calculate the square root of the right side: 4.543195461 Break this problem into two subproblems by setting (x + -3.625) equal to 4.543195461 and -4.543195461.Subproblem 1
x + -3.625 = 4.543195461 Simplifying x + -3.625 = 4.543195461 Reorder the terms: -3.625 + x = 4.543195461 Solving -3.625 + x = 4.543195461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 4.543195461 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 4.543195461 + 3.625 x = 4.543195461 + 3.625 Combine like terms: 4.543195461 + 3.625 = 8.168195461 x = 8.168195461 Simplifying x = 8.168195461Subproblem 2
x + -3.625 = -4.543195461 Simplifying x + -3.625 = -4.543195461 Reorder the terms: -3.625 + x = -4.543195461 Solving -3.625 + x = -4.543195461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -4.543195461 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -4.543195461 + 3.625 x = -4.543195461 + 3.625 Combine like terms: -4.543195461 + 3.625 = -0.918195461 x = -0.918195461 Simplifying x = -0.918195461Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.168195461, -0.918195461}
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