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Simplifying 4x2 + -51x + 147 = 0 Reorder the terms: 147 + -51x + 4x2 = 0 Solving 147 + -51x + 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'. 36.75 + -12.75x + x2 = 0 Move the constant term to the right: Add '-36.75' to each side of the equation. 36.75 + -12.75x + -36.75 + x2 = 0 + -36.75 Reorder the terms: 36.75 + -36.75 + -12.75x + x2 = 0 + -36.75 Combine like terms: 36.75 + -36.75 = 0.00 0.00 + -12.75x + x2 = 0 + -36.75 -12.75x + x2 = 0 + -36.75 Combine like terms: 0 + -36.75 = -36.75 -12.75x + x2 = -36.75 The x term is -12.75x. Take half its coefficient (-6.375). Square it (40.640625) and add it to both sides. Add '40.640625' to each side of the equation. -12.75x + 40.640625 + x2 = -36.75 + 40.640625 Reorder the terms: 40.640625 + -12.75x + x2 = -36.75 + 40.640625 Combine like terms: -36.75 + 40.640625 = 3.890625 40.640625 + -12.75x + x2 = 3.890625 Factor a perfect square on the left side: (x + -6.375)(x + -6.375) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (x + -6.375) equal to 1.97246673 and -1.97246673.Subproblem 1
x + -6.375 = 1.97246673 Simplifying x + -6.375 = 1.97246673 Reorder the terms: -6.375 + x = 1.97246673 Solving -6.375 + x = 1.97246673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.375' to each side of the equation. -6.375 + 6.375 + x = 1.97246673 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + x = 1.97246673 + 6.375 x = 1.97246673 + 6.375 Combine like terms: 1.97246673 + 6.375 = 8.34746673 x = 8.34746673 Simplifying x = 8.34746673Subproblem 2
x + -6.375 = -1.97246673 Simplifying x + -6.375 = -1.97246673 Reorder the terms: -6.375 + x = -1.97246673 Solving -6.375 + x = -1.97246673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.375' to each side of the equation. -6.375 + 6.375 + x = -1.97246673 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + x = -1.97246673 + 6.375 x = -1.97246673 + 6.375 Combine like terms: -1.97246673 + 6.375 = 4.40253327 x = 4.40253327 Simplifying x = 4.40253327Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.34746673, 4.40253327}
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