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Simplifying 4x2 + -19x + -51 = 0 Reorder the terms: -51 + -19x + 4x2 = 0 Solving -51 + -19x + 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'. -12.75 + -4.75x + x2 = 0 Move the constant term to the right: Add '12.75' to each side of the equation. -12.75 + -4.75x + 12.75 + x2 = 0 + 12.75 Reorder the terms: -12.75 + 12.75 + -4.75x + x2 = 0 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + -4.75x + x2 = 0 + 12.75 -4.75x + x2 = 0 + 12.75 Combine like terms: 0 + 12.75 = 12.75 -4.75x + x2 = 12.75 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = 12.75 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 12.75 + 5.640625 Combine like terms: 12.75 + 5.640625 = 18.390625 5.640625 + -4.75x + x2 = 18.390625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 18.390625 Calculate the square root of the right side: 4.2884292 Break this problem into two subproblems by setting (x + -2.375) equal to 4.2884292 and -4.2884292.Subproblem 1
x + -2.375 = 4.2884292 Simplifying x + -2.375 = 4.2884292 Reorder the terms: -2.375 + x = 4.2884292 Solving -2.375 + x = 4.2884292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 4.2884292 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 4.2884292 + 2.375 x = 4.2884292 + 2.375 Combine like terms: 4.2884292 + 2.375 = 6.6634292 x = 6.6634292 Simplifying x = 6.6634292Subproblem 2
x + -2.375 = -4.2884292 Simplifying x + -2.375 = -4.2884292 Reorder the terms: -2.375 + x = -4.2884292 Solving -2.375 + x = -4.2884292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -4.2884292 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -4.2884292 + 2.375 x = -4.2884292 + 2.375 Combine like terms: -4.2884292 + 2.375 = -1.9134292 x = -1.9134292 Simplifying x = -1.9134292Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.6634292, -1.9134292}
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