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Simplifying 0.4 = 5.5x + -4.9x2 Solving 0.4 = 5.5x + -4.9x2 Solving for variable 'x'. Reorder the terms: 0.4 + -5.5x + 4.9x2 = 5.5x + -5.5x + -4.9x2 + 4.9x2 Combine like terms: 5.5x + -5.5x = 0.0 0.4 + -5.5x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 0.4 + -5.5x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 0.4 + -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'. 0.08163265306 + -1.12244898x + x2 = 0 Move the constant term to the right: Add '-0.08163265306' to each side of the equation. 0.08163265306 + -1.12244898x + -0.08163265306 + x2 = 0 + -0.08163265306 Reorder the terms: 0.08163265306 + -0.08163265306 + -1.12244898x + x2 = 0 + -0.08163265306 Combine like terms: 0.08163265306 + -0.08163265306 = 0.00000000000 0.00000000000 + -1.12244898x + x2 = 0 + -0.08163265306 -1.12244898x + x2 = 0 + -0.08163265306 Combine like terms: 0 + -0.08163265306 = -0.08163265306 -1.12244898x + x2 = -0.08163265306 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 = -0.08163265306 + 0.3149729282 Reorder the terms: 0.3149729282 + -1.12244898x + x2 = -0.08163265306 + 0.3149729282 Combine like terms: -0.08163265306 + 0.3149729282 = 0.23334027514 0.3149729282 + -1.12244898x + x2 = 0.23334027514 Factor a perfect square on the left side: (x + -0.56122449)(x + -0.56122449) = 0.23334027514 Calculate the square root of the right side: 0.483053077 Break this problem into two subproblems by setting (x + -0.56122449) equal to 0.483053077 and -0.483053077.Subproblem 1
x + -0.56122449 = 0.483053077 Simplifying x + -0.56122449 = 0.483053077 Reorder the terms: -0.56122449 + x = 0.483053077 Solving -0.56122449 + x = 0.483053077 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 = 0.483053077 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + x = 0.483053077 + 0.56122449 x = 0.483053077 + 0.56122449 Combine like terms: 0.483053077 + 0.56122449 = 1.044277567 x = 1.044277567 Simplifying x = 1.044277567Subproblem 2
x + -0.56122449 = -0.483053077 Simplifying x + -0.56122449 = -0.483053077 Reorder the terms: -0.56122449 + x = -0.483053077 Solving -0.56122449 + x = -0.483053077 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 = -0.483053077 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + x = -0.483053077 + 0.56122449 x = -0.483053077 + 0.56122449 Combine like terms: -0.483053077 + 0.56122449 = 0.078171413 x = 0.078171413 Simplifying x = 0.078171413Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.044277567, 0.078171413}
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