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Simplifying 3 + -14x = 11 + -7x[22.3 + 7x] 3 + -14x = 11 + [22.3 * -7x + 7x * -7x] 3 + -14x = 11 + [-156.1x + -49x2] Solving 3 + -14x = 11 + -156.1x + -49x2 Solving for variable 'x'. Reorder the terms: 3 + -11 + -14x + 156.1x + 49x2 = 11 + -156.1x + -49x2 + -11 + 156.1x + 49x2 Combine like terms: 3 + -11 = -8 -8 + -14x + 156.1x + 49x2 = 11 + -156.1x + -49x2 + -11 + 156.1x + 49x2 Combine like terms: -14x + 156.1x = 142.1x -8 + 142.1x + 49x2 = 11 + -156.1x + -49x2 + -11 + 156.1x + 49x2 Reorder the terms: -8 + 142.1x + 49x2 = 11 + -11 + -156.1x + 156.1x + -49x2 + 49x2 Combine like terms: 11 + -11 = 0 -8 + 142.1x + 49x2 = 0 + -156.1x + 156.1x + -49x2 + 49x2 -8 + 142.1x + 49x2 = -156.1x + 156.1x + -49x2 + 49x2 Combine like terms: -156.1x + 156.1x = 0.0 -8 + 142.1x + 49x2 = 0.0 + -49x2 + 49x2 -8 + 142.1x + 49x2 = -49x2 + 49x2 Combine like terms: -49x2 + 49x2 = 0 -8 + 142.1x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.1632653061 + 2.9x + x2 = 0 Move the constant term to the right: Add '0.1632653061' to each side of the equation. -0.1632653061 + 2.9x + 0.1632653061 + x2 = 0 + 0.1632653061 Reorder the terms: -0.1632653061 + 0.1632653061 + 2.9x + x2 = 0 + 0.1632653061 Combine like terms: -0.1632653061 + 0.1632653061 = 0.0000000000 0.0000000000 + 2.9x + x2 = 0 + 0.1632653061 2.9x + x2 = 0 + 0.1632653061 Combine like terms: 0 + 0.1632653061 = 0.1632653061 2.9x + x2 = 0.1632653061 The x term is 2.9x. Take half its coefficient (1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. 2.9x + 2.1025 + x2 = 0.1632653061 + 2.1025 Reorder the terms: 2.1025 + 2.9x + x2 = 0.1632653061 + 2.1025 Combine like terms: 0.1632653061 + 2.1025 = 2.2657653061 2.1025 + 2.9x + x2 = 2.2657653061 Factor a perfect square on the left side: (x + 1.45)(x + 1.45) = 2.2657653061 Calculate the square root of the right side: 1.505245929 Break this problem into two subproblems by setting (x + 1.45) equal to 1.505245929 and -1.505245929.Subproblem 1
x + 1.45 = 1.505245929 Simplifying x + 1.45 = 1.505245929 Reorder the terms: 1.45 + x = 1.505245929 Solving 1.45 + x = 1.505245929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.45' to each side of the equation. 1.45 + -1.45 + x = 1.505245929 + -1.45 Combine like terms: 1.45 + -1.45 = 0.00 0.00 + x = 1.505245929 + -1.45 x = 1.505245929 + -1.45 Combine like terms: 1.505245929 + -1.45 = 0.055245929 x = 0.055245929 Simplifying x = 0.055245929Subproblem 2
x + 1.45 = -1.505245929 Simplifying x + 1.45 = -1.505245929 Reorder the terms: 1.45 + x = -1.505245929 Solving 1.45 + x = -1.505245929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.45' to each side of the equation. 1.45 + -1.45 + x = -1.505245929 + -1.45 Combine like terms: 1.45 + -1.45 = 0.00 0.00 + x = -1.505245929 + -1.45 x = -1.505245929 + -1.45 Combine like terms: -1.505245929 + -1.45 = -2.955245929 x = -2.955245929 Simplifying x = -2.955245929Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.055245929, -2.955245929}
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