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Simplifying 0 = x2 + 8x + -75 Reorder the terms: 0 = -75 + 8x + x2 Solving 0 = -75 + 8x + x2 Solving for variable 'x'. Combine like terms: 0 + 75 = 75 75 + -8x + -1x2 = -75 + 8x + x2 + 75 + -8x + -1x2 Reorder the terms: 75 + -8x + -1x2 = -75 + 75 + 8x + -8x + x2 + -1x2 Combine like terms: -75 + 75 = 0 75 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 75 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 75 + -8x + -1x2 = 0 + x2 + -1x2 75 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 75 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -75 + 8x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 8x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 8x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 8x + x2 = 0 + 75 8x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 8x + x2 = 75 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 75 + 16 Reorder the terms: 16 + 8x + x2 = 75 + 16 Combine like terms: 75 + 16 = 91 16 + 8x + x2 = 91 Factor a perfect square on the left side: (x + 4)(x + 4) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + 4) equal to 9.539392014 and -9.539392014.Subproblem 1
x + 4 = 9.539392014 Simplifying x + 4 = 9.539392014 Reorder the terms: 4 + x = 9.539392014 Solving 4 + x = 9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 9.539392014 + -4 Combine like terms: 4 + -4 = 0 0 + x = 9.539392014 + -4 x = 9.539392014 + -4 Combine like terms: 9.539392014 + -4 = 5.539392014 x = 5.539392014 Simplifying x = 5.539392014Subproblem 2
x + 4 = -9.539392014 Simplifying x + 4 = -9.539392014 Reorder the terms: 4 + x = -9.539392014 Solving 4 + x = -9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -9.539392014 + -4 Combine like terms: 4 + -4 = 0 0 + x = -9.539392014 + -4 x = -9.539392014 + -4 Combine like terms: -9.539392014 + -4 = -13.539392014 x = -13.539392014 Simplifying x = -13.539392014Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.539392014, -13.539392014}
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