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Simplifying (4x2 + -6) + (-2x + 19x) = 180 Reorder the terms: (-6 + 4x2) + (-2x + 19x) = 180 Remove parenthesis around (-6 + 4x2) -6 + 4x2 + (-2x + 19x) = 180 Combine like terms: -2x + 19x = 17x -6 + 4x2 + (17x) = 180 -6 + 4x2 + (17x) = 180 Reorder the terms: -6 + (17x) + 4x2 = 180 Solving -6 + (17x) + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -6 + -180 + (17x) + 4x2 = 180 + -180 Combine like terms: -6 + -180 = -186 -186 + (17x) + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -186 + (17x) + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -46.5 + (4.25x) + x2 = 0 Move the constant term to the right: Add '46.5' to each side of the equation. -46.5 + (4.25x) + 46.5 + x2 = 0 + 46.5 Reorder the terms: -46.5 + 46.5 + (4.25x) + x2 = 0 + 46.5 Combine like terms: -46.5 + 46.5 = 0.0 0.0 + (4.25x) + x2 = 0 + 46.5 (4.25x) + x2 = 0 + 46.5 Combine like terms: 0 + 46.5 = 46.5 (4.25x) + x2 = 46.5 The x term is (4.25x). Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. (4.25x) + 4.515625 + x2 = 46.5 + 4.515625 Reorder the terms: 4.515625 + (4.25x) + x2 = 46.5 + 4.515625 Combine like terms: 46.5 + 4.515625 = 51.015625 4.515625 + (4.25x) + x2 = 51.015625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 51.015625 Calculate the square root of the right side: 7.142522314 Break this problem into two subproblems by setting (x + 2.125) equal to 7.142522314 and -7.142522314.Subproblem 1
x + 2.125 = 7.142522314 Simplifying x + 2.125 = 7.142522314 Reorder the terms: 2.125 + x = 7.142522314 Solving 2.125 + x = 7.142522314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 7.142522314 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 7.142522314 + -2.125 x = 7.142522314 + -2.125 Combine like terms: 7.142522314 + -2.125 = 5.017522314 x = 5.017522314 Simplifying x = 5.017522314Subproblem 2
x + 2.125 = -7.142522314 Simplifying x + 2.125 = -7.142522314 Reorder the terms: 2.125 + x = -7.142522314 Solving 2.125 + x = -7.142522314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -7.142522314 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -7.142522314 + -2.125 x = -7.142522314 + -2.125 Combine like terms: -7.142522314 + -2.125 = -9.267522314 x = -9.267522314 Simplifying x = -9.267522314Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.017522314, -9.267522314}
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