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Simplifying 0 = 8x2 + 25x + -42 Reorder the terms: 0 = -42 + 25x + 8x2 Solving 0 = -42 + 25x + 8x2 Solving for variable 'x'. Combine like terms: 0 + 42 = 42 42 + -25x + -8x2 = -42 + 25x + 8x2 + 42 + -25x + -8x2 Reorder the terms: 42 + -25x + -8x2 = -42 + 42 + 25x + -25x + 8x2 + -8x2 Combine like terms: -42 + 42 = 0 42 + -25x + -8x2 = 0 + 25x + -25x + 8x2 + -8x2 42 + -25x + -8x2 = 25x + -25x + 8x2 + -8x2 Combine like terms: 25x + -25x = 0 42 + -25x + -8x2 = 0 + 8x2 + -8x2 42 + -25x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 42 + -25x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -5.25 + 3.125x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 3.125x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 3.125x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 3.125x + x2 = 0 + 5.25 3.125x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 3.125x + x2 = 5.25 The x term is 3.125x. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125x + 2.44140625 + x2 = 5.25 + 2.44140625 Reorder the terms: 2.44140625 + 3.125x + x2 = 5.25 + 2.44140625 Combine like terms: 5.25 + 2.44140625 = 7.69140625 2.44140625 + 3.125x + x2 = 7.69140625 Factor a perfect square on the left side: (x + 1.5625)(x + 1.5625) = 7.69140625 Calculate the square root of the right side: 2.773338467 Break this problem into two subproblems by setting (x + 1.5625) equal to 2.773338467 and -2.773338467.Subproblem 1
x + 1.5625 = 2.773338467 Simplifying x + 1.5625 = 2.773338467 Reorder the terms: 1.5625 + x = 2.773338467 Solving 1.5625 + x = 2.773338467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = 2.773338467 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = 2.773338467 + -1.5625 x = 2.773338467 + -1.5625 Combine like terms: 2.773338467 + -1.5625 = 1.210838467 x = 1.210838467 Simplifying x = 1.210838467Subproblem 2
x + 1.5625 = -2.773338467 Simplifying x + 1.5625 = -2.773338467 Reorder the terms: 1.5625 + x = -2.773338467 Solving 1.5625 + x = -2.773338467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = -2.773338467 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = -2.773338467 + -1.5625 x = -2.773338467 + -1.5625 Combine like terms: -2.773338467 + -1.5625 = -4.335838467 x = -4.335838467 Simplifying x = -4.335838467Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.210838467, -4.335838467}
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