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Simplifying 2.9x2 + 9.4x + -5.2 = 0 Reorder the terms: -5.2 + 9.4x + 2.9x2 = 0 Solving -5.2 + 9.4x + 2.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.9 the coefficient of the squared term: Divide each side by '2.9'. -1.793103448 + 3.24137931x + x2 = 0 Move the constant term to the right: Add '1.793103448' to each side of the equation. -1.793103448 + 3.24137931x + 1.793103448 + x2 = 0 + 1.793103448 Reorder the terms: -1.793103448 + 1.793103448 + 3.24137931x + x2 = 0 + 1.793103448 Combine like terms: -1.793103448 + 1.793103448 = 0.000000000 0.000000000 + 3.24137931x + x2 = 0 + 1.793103448 3.24137931x + x2 = 0 + 1.793103448 Combine like terms: 0 + 1.793103448 = 1.793103448 3.24137931x + x2 = 1.793103448 The x term is 3.24137931x. Take half its coefficient (1.620689655). Square it (2.626634958) and add it to both sides. Add '2.626634958' to each side of the equation. 3.24137931x + 2.626634958 + x2 = 1.793103448 + 2.626634958 Reorder the terms: 2.626634958 + 3.24137931x + x2 = 1.793103448 + 2.626634958 Combine like terms: 1.793103448 + 2.626634958 = 4.419738406 2.626634958 + 3.24137931x + x2 = 4.419738406 Factor a perfect square on the left side: (x + 1.620689655)(x + 1.620689655) = 4.419738406 Calculate the square root of the right side: 2.102317389 Break this problem into two subproblems by setting (x + 1.620689655) equal to 2.102317389 and -2.102317389.Subproblem 1
x + 1.620689655 = 2.102317389 Simplifying x + 1.620689655 = 2.102317389 Reorder the terms: 1.620689655 + x = 2.102317389 Solving 1.620689655 + x = 2.102317389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.620689655' to each side of the equation. 1.620689655 + -1.620689655 + x = 2.102317389 + -1.620689655 Combine like terms: 1.620689655 + -1.620689655 = 0.000000000 0.000000000 + x = 2.102317389 + -1.620689655 x = 2.102317389 + -1.620689655 Combine like terms: 2.102317389 + -1.620689655 = 0.481627734 x = 0.481627734 Simplifying x = 0.481627734Subproblem 2
x + 1.620689655 = -2.102317389 Simplifying x + 1.620689655 = -2.102317389 Reorder the terms: 1.620689655 + x = -2.102317389 Solving 1.620689655 + x = -2.102317389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.620689655' to each side of the equation. 1.620689655 + -1.620689655 + x = -2.102317389 + -1.620689655 Combine like terms: 1.620689655 + -1.620689655 = 0.000000000 0.000000000 + x = -2.102317389 + -1.620689655 x = -2.102317389 + -1.620689655 Combine like terms: -2.102317389 + -1.620689655 = -3.723007044 x = -3.723007044 Simplifying x = -3.723007044Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.481627734, -3.723007044}
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