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Simplifying 0 = 0.375x2 + 21x + -80 Reorder the terms: 0 = -80 + 21x + 0.375x2 Solving 0 = -80 + 21x + 0.375x2 Solving for variable 'x'. Combine like terms: 0 + 80 = 80 80 + -21x + -0.375x2 = -80 + 21x + 0.375x2 + 80 + -21x + -0.375x2 Reorder the terms: 80 + -21x + -0.375x2 = -80 + 80 + 21x + -21x + 0.375x2 + -0.375x2 Combine like terms: -80 + 80 = 0 80 + -21x + -0.375x2 = 0 + 21x + -21x + 0.375x2 + -0.375x2 80 + -21x + -0.375x2 = 21x + -21x + 0.375x2 + -0.375x2 Combine like terms: 21x + -21x = 0 80 + -21x + -0.375x2 = 0 + 0.375x2 + -0.375x2 80 + -21x + -0.375x2 = 0.375x2 + -0.375x2 Combine like terms: 0.375x2 + -0.375x2 = 0.000 80 + -21x + -0.375x2 = 0.000 Begin completing the square. Divide all terms by -0.375 the coefficient of the squared term: Divide each side by '-0.375'. -213.3333333 + 56x + x2 = 0 Move the constant term to the right: Add '213.3333333' to each side of the equation. -213.3333333 + 56x + 213.3333333 + x2 = 0 + 213.3333333 Reorder the terms: -213.3333333 + 213.3333333 + 56x + x2 = 0 + 213.3333333 Combine like terms: -213.3333333 + 213.3333333 = 0.0000000 0.0000000 + 56x + x2 = 0 + 213.3333333 56x + x2 = 0 + 213.3333333 Combine like terms: 0 + 213.3333333 = 213.3333333 56x + x2 = 213.3333333 The x term is 56x. Take half its coefficient (28). Square it (784) and add it to both sides. Add '784' to each side of the equation. 56x + 784 + x2 = 213.3333333 + 784 Reorder the terms: 784 + 56x + x2 = 213.3333333 + 784 Combine like terms: 213.3333333 + 784 = 997.3333333 784 + 56x + x2 = 997.3333333 Factor a perfect square on the left side: (x + 28)(x + 28) = 997.3333333 Calculate the square root of the right side: 31.580584752 Break this problem into two subproblems by setting (x + 28) equal to 31.580584752 and -31.580584752.Subproblem 1
x + 28 = 31.580584752 Simplifying x + 28 = 31.580584752 Reorder the terms: 28 + x = 31.580584752 Solving 28 + x = 31.580584752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = 31.580584752 + -28 Combine like terms: 28 + -28 = 0 0 + x = 31.580584752 + -28 x = 31.580584752 + -28 Combine like terms: 31.580584752 + -28 = 3.580584752 x = 3.580584752 Simplifying x = 3.580584752Subproblem 2
x + 28 = -31.580584752 Simplifying x + 28 = -31.580584752 Reorder the terms: 28 + x = -31.580584752 Solving 28 + x = -31.580584752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = -31.580584752 + -28 Combine like terms: 28 + -28 = 0 0 + x = -31.580584752 + -28 x = -31.580584752 + -28 Combine like terms: -31.580584752 + -28 = -59.580584752 x = -59.580584752 Simplifying x = -59.580584752Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.580584752, -59.580584752}
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