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Simplifying (0.420)(7.2 + -1x)(4.8 + -1x) = (x)(6.4 + x) Multiply (7.2 + -1x) * (4.8 + -1x) 0.420(7.2(4.8 + -1x) + -1x * (4.8 + -1x)) = (x)(6.4 + x) 0.420((4.8 * 7.2 + -1x * 7.2) + -1x * (4.8 + -1x)) = (x)(6.4 + x) 0.420((34.56 + -7.2x) + -1x * (4.8 + -1x)) = (x)(6.4 + x) 0.420(34.56 + -7.2x + (4.8 * -1x + -1x * -1x)) = (x)(6.4 + x) 0.420(34.56 + -7.2x + (-4.8x + 1x2)) = (x)(6.4 + x) Combine like terms: -7.2x + -4.8x = -12x 0.420(34.56 + -12x + 1x2) = (x)(6.4 + x) (34.56 * 0.420 + -12x * 0.420 + 1x2 * 0.420) = (x)(6.4 + x) (14.5152 + -5.04x + 0.42x2) = (x)(6.4 + x) 14.5152 + -5.04x + 0.42x2 = (6.4 * x + x * x) 14.5152 + -5.04x + 0.42x2 = (6.4x + x2) Solving 14.5152 + -5.04x + 0.42x2 = 6.4x + x2 Solving for variable 'x'. Reorder the terms: 14.5152 + -5.04x + -6.4x + 0.42x2 + -1x2 = 6.4x + x2 + -6.4x + -1x2 Combine like terms: -5.04x + -6.4x = -11.44x 14.5152 + -11.44x + 0.42x2 + -1x2 = 6.4x + x2 + -6.4x + -1x2 Combine like terms: 0.42x2 + -1x2 = -0.58x2 14.5152 + -11.44x + -0.58x2 = 6.4x + x2 + -6.4x + -1x2 Reorder the terms: 14.5152 + -11.44x + -0.58x2 = 6.4x + -6.4x + x2 + -1x2 Combine like terms: 6.4x + -6.4x = 0.0 14.5152 + -11.44x + -0.58x2 = 0.0 + x2 + -1x2 14.5152 + -11.44x + -0.58x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 14.5152 + -11.44x + -0.58x2 = 0 Begin completing the square. Divide all terms by -0.58 the coefficient of the squared term: Divide each side by '-0.58'. -25.0262069 + 19.72413793x + x2 = 0 Move the constant term to the right: Add '25.0262069' to each side of the equation. -25.0262069 + 19.72413793x + 25.0262069 + x2 = 0 + 25.0262069 Reorder the terms: -25.0262069 + 25.0262069 + 19.72413793x + x2 = 0 + 25.0262069 Combine like terms: -25.0262069 + 25.0262069 = 0.0000000 0.0000000 + 19.72413793x + x2 = 0 + 25.0262069 19.72413793x + x2 = 0 + 25.0262069 Combine like terms: 0 + 25.0262069 = 25.0262069 19.72413793x + x2 = 25.0262069 The x term is 19.72413793x. Take half its coefficient (9.862068965). Square it (97.26040427) and add it to both sides. Add '97.26040427' to each side of the equation. 19.72413793x + 97.26040427 + x2 = 25.0262069 + 97.26040427 Reorder the terms: 97.26040427 + 19.72413793x + x2 = 25.0262069 + 97.26040427 Combine like terms: 25.0262069 + 97.26040427 = 122.28661117 97.26040427 + 19.72413793x + x2 = 122.28661117 Factor a perfect square on the left side: (x + 9.862068965)(x + 9.862068965) = 122.28661117 Calculate the square root of the right side: 11.058327684 Break this problem into two subproblems by setting (x + 9.862068965) equal to 11.058327684 and -11.058327684.Subproblem 1
x + 9.862068965 = 11.058327684 Simplifying x + 9.862068965 = 11.058327684 Reorder the terms: 9.862068965 + x = 11.058327684 Solving 9.862068965 + x = 11.058327684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.862068965' to each side of the equation. 9.862068965 + -9.862068965 + x = 11.058327684 + -9.862068965 Combine like terms: 9.862068965 + -9.862068965 = 0.000000000 0.000000000 + x = 11.058327684 + -9.862068965 x = 11.058327684 + -9.862068965 Combine like terms: 11.058327684 + -9.862068965 = 1.196258719 x = 1.196258719 Simplifying x = 1.196258719Subproblem 2
x + 9.862068965 = -11.058327684 Simplifying x + 9.862068965 = -11.058327684 Reorder the terms: 9.862068965 + x = -11.058327684 Solving 9.862068965 + x = -11.058327684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.862068965' to each side of the equation. 9.862068965 + -9.862068965 + x = -11.058327684 + -9.862068965 Combine like terms: 9.862068965 + -9.862068965 = 0.000000000 0.000000000 + x = -11.058327684 + -9.862068965 x = -11.058327684 + -9.862068965 Combine like terms: -11.058327684 + -9.862068965 = -20.920396649 x = -20.920396649 Simplifying x = -20.920396649Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.196258719, -20.920396649}
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