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Simplifying 10 = 5.5x + -4.9(x2) + 9 Reorder the terms: 10 = 9 + 5.5x + -4.9x2 Solving 10 = 9 + 5.5x + -4.9x2 Solving for variable 'x'. Combine like terms: 10 + -9 = 1 1 + -5.5x + 4.9x2 = 9 + 5.5x + -4.9x2 + -9 + -5.5x + 4.9x2 Reorder the terms: 1 + -5.5x + 4.9x2 = 9 + -9 + 5.5x + -5.5x + -4.9x2 + 4.9x2 Combine like terms: 9 + -9 = 0 1 + -5.5x + 4.9x2 = 0 + 5.5x + -5.5x + -4.9x2 + 4.9x2 1 + -5.5x + 4.9x2 = 5.5x + -5.5x + -4.9x2 + 4.9x2 Combine like terms: 5.5x + -5.5x = 0.0 1 + -5.5x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 1 + -5.5x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 1 + -5.5x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.2040816327 + -1.12244898x + x2 = 0 Move the constant term to the right: Add '-0.2040816327' to each side of the equation. 0.2040816327 + -1.12244898x + -0.2040816327 + x2 = 0 + -0.2040816327 Reorder the terms: 0.2040816327 + -0.2040816327 + -1.12244898x + x2 = 0 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + -1.12244898x + x2 = 0 + -0.2040816327 -1.12244898x + x2 = 0 + -0.2040816327 Combine like terms: 0 + -0.2040816327 = -0.2040816327 -1.12244898x + x2 = -0.2040816327 The x term is -1.12244898x. Take half its coefficient (-0.56122449). Square it (0.3149729282) and add it to both sides. Add '0.3149729282' to each side of the equation. -1.12244898x + 0.3149729282 + x2 = -0.2040816327 + 0.3149729282 Reorder the terms: 0.3149729282 + -1.12244898x + x2 = -0.2040816327 + 0.3149729282 Combine like terms: -0.2040816327 + 0.3149729282 = 0.1108912955 0.3149729282 + -1.12244898x + x2 = 0.1108912955 Factor a perfect square on the left side: (x + -0.56122449)(x + -0.56122449) = 0.1108912955 Calculate the square root of the right side: 0.333003447 Break this problem into two subproblems by setting (x + -0.56122449) equal to 0.333003447 and -0.333003447.Subproblem 1
x + -0.56122449 = 0.333003447 Simplifying x + -0.56122449 = 0.333003447 Reorder the terms: -0.56122449 + x = 0.333003447 Solving -0.56122449 + x = 0.333003447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + x = 0.333003447 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + x = 0.333003447 + 0.56122449 x = 0.333003447 + 0.56122449 Combine like terms: 0.333003447 + 0.56122449 = 0.894227937 x = 0.894227937 Simplifying x = 0.894227937Subproblem 2
x + -0.56122449 = -0.333003447 Simplifying x + -0.56122449 = -0.333003447 Reorder the terms: -0.56122449 + x = -0.333003447 Solving -0.56122449 + x = -0.333003447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + x = -0.333003447 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + x = -0.333003447 + 0.56122449 x = -0.333003447 + 0.56122449 Combine like terms: -0.333003447 + 0.56122449 = 0.228221043 x = 0.228221043 Simplifying x = 0.228221043Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.894227937, 0.228221043}
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