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Simplifying 4x2 + 19x + -45 = 0 Reorder the terms: -45 + 19x + 4x2 = 0 Solving -45 + 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'. -11.25 + 4.75x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + 4.75x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + 4.75x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + 4.75x + x2 = 0 + 11.25 4.75x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 4.75x + x2 = 11.25 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 = 11.25 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 11.25 + 5.640625 Combine like terms: 11.25 + 5.640625 = 16.890625 5.640625 + 4.75x + x2 = 16.890625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 16.890625 Calculate the square root of the right side: 4.109820556 Break this problem into two subproblems by setting (x + 2.375) equal to 4.109820556 and -4.109820556.Subproblem 1
x + 2.375 = 4.109820556 Simplifying x + 2.375 = 4.109820556 Reorder the terms: 2.375 + x = 4.109820556 Solving 2.375 + x = 4.109820556 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 = 4.109820556 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 4.109820556 + -2.375 x = 4.109820556 + -2.375 Combine like terms: 4.109820556 + -2.375 = 1.734820556 x = 1.734820556 Simplifying x = 1.734820556Subproblem 2
x + 2.375 = -4.109820556 Simplifying x + 2.375 = -4.109820556 Reorder the terms: 2.375 + x = -4.109820556 Solving 2.375 + x = -4.109820556 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 = -4.109820556 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -4.109820556 + -2.375 x = -4.109820556 + -2.375 Combine like terms: -4.109820556 + -2.375 = -6.484820556 x = -6.484820556 Simplifying x = -6.484820556Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.734820556, -6.484820556}
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