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Simplifying 0 = x2 + 4.4x + -15.41 Reorder the terms: 0 = -15.41 + 4.4x + x2 Solving 0 = -15.41 + 4.4x + x2 Solving for variable 'x'. Combine like terms: 0 + 15.41 = 15.41 15.41 + -4.4x + -1x2 = -15.41 + 4.4x + x2 + 15.41 + -4.4x + -1x2 Reorder the terms: 15.41 + -4.4x + -1x2 = -15.41 + 15.41 + 4.4x + -4.4x + x2 + -1x2 Combine like terms: -15.41 + 15.41 = 0.00 15.41 + -4.4x + -1x2 = 0.00 + 4.4x + -4.4x + x2 + -1x2 15.41 + -4.4x + -1x2 = 4.4x + -4.4x + x2 + -1x2 Combine like terms: 4.4x + -4.4x = 0.0 15.41 + -4.4x + -1x2 = 0.0 + x2 + -1x2 15.41 + -4.4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15.41 + -4.4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15.41 + 4.4x + x2 = 0 Move the constant term to the right: Add '15.41' to each side of the equation. -15.41 + 4.4x + 15.41 + x2 = 0 + 15.41 Reorder the terms: -15.41 + 15.41 + 4.4x + x2 = 0 + 15.41 Combine like terms: -15.41 + 15.41 = 0.00 0.00 + 4.4x + x2 = 0 + 15.41 4.4x + x2 = 0 + 15.41 Combine like terms: 0 + 15.41 = 15.41 4.4x + x2 = 15.41 The x term is 4.4x. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4x + 4.84 + x2 = 15.41 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = 15.41 + 4.84 Combine like terms: 15.41 + 4.84 = 20.25 4.84 + 4.4x + x2 = 20.25 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = 20.25 Calculate the square root of the right side: 4.5 Break this problem into two subproblems by setting (x + 2.2) equal to 4.5 and -4.5.Subproblem 1
x + 2.2 = 4.5 Simplifying x + 2.2 = 4.5 Reorder the terms: 2.2 + x = 4.5 Solving 2.2 + x = 4.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = 4.5 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 4.5 + -2.2 x = 4.5 + -2.2 Combine like terms: 4.5 + -2.2 = 2.3 x = 2.3 Simplifying x = 2.3Subproblem 2
x + 2.2 = -4.5 Simplifying x + 2.2 = -4.5 Reorder the terms: 2.2 + x = -4.5 Solving 2.2 + x = -4.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = -4.5 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -4.5 + -2.2 x = -4.5 + -2.2 Combine like terms: -4.5 + -2.2 = -6.7 x = -6.7 Simplifying x = -6.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3, -6.7}
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