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Simplifying 4x2 + 19x + -6 = 180 Reorder the terms: -6 + 19x + 4x2 = 180 Solving -6 + 19x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -6 + -180 + 19x + 4x2 = 180 + -180 Combine like terms: -6 + -180 = -186 -186 + 19x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -186 + 19x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -46.5 + 4.75x + x2 = 0 Move the constant term to the right: Add '46.5' to each side of the equation. -46.5 + 4.75x + 46.5 + x2 = 0 + 46.5 Reorder the terms: -46.5 + 46.5 + 4.75x + x2 = 0 + 46.5 Combine like terms: -46.5 + 46.5 = 0.0 0.0 + 4.75x + x2 = 0 + 46.5 4.75x + x2 = 0 + 46.5 Combine like terms: 0 + 46.5 = 46.5 4.75x + x2 = 46.5 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 = 46.5 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 46.5 + 5.640625 Combine like terms: 46.5 + 5.640625 = 52.140625 5.640625 + 4.75x + x2 = 52.140625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 52.140625 Calculate the square root of the right side: 7.220846557 Break this problem into two subproblems by setting (x + 2.375) equal to 7.220846557 and -7.220846557.Subproblem 1
x + 2.375 = 7.220846557 Simplifying x + 2.375 = 7.220846557 Reorder the terms: 2.375 + x = 7.220846557 Solving 2.375 + x = 7.220846557 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 = 7.220846557 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 7.220846557 + -2.375 x = 7.220846557 + -2.375 Combine like terms: 7.220846557 + -2.375 = 4.845846557 x = 4.845846557 Simplifying x = 4.845846557Subproblem 2
x + 2.375 = -7.220846557 Simplifying x + 2.375 = -7.220846557 Reorder the terms: 2.375 + x = -7.220846557 Solving 2.375 + x = -7.220846557 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 = -7.220846557 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -7.220846557 + -2.375 x = -7.220846557 + -2.375 Combine like terms: -7.220846557 + -2.375 = -9.595846557 x = -9.595846557 Simplifying x = -9.595846557Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.845846557, -9.595846557}
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