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Simplifying 8x2 + -7x + -120 = 0 Reorder the terms: -120 + -7x + 8x2 = 0 Solving -120 + -7x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -15 + -0.875x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -0.875x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -0.875x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -0.875x + x2 = 0 + 15 -0.875x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -0.875x + x2 = 15 The x term is -0.875x. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875x + 0.19140625 + x2 = 15 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 15 + 0.19140625 Combine like terms: 15 + 0.19140625 = 15.19140625 0.19140625 + -0.875x + x2 = 15.19140625 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 15.19140625 Calculate the square root of the right side: 3.897615457 Break this problem into two subproblems by setting (x + -0.4375) equal to 3.897615457 and -3.897615457.Subproblem 1
x + -0.4375 = 3.897615457 Simplifying x + -0.4375 = 3.897615457 Reorder the terms: -0.4375 + x = 3.897615457 Solving -0.4375 + x = 3.897615457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 3.897615457 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 3.897615457 + 0.4375 x = 3.897615457 + 0.4375 Combine like terms: 3.897615457 + 0.4375 = 4.335115457 x = 4.335115457 Simplifying x = 4.335115457Subproblem 2
x + -0.4375 = -3.897615457 Simplifying x + -0.4375 = -3.897615457 Reorder the terms: -0.4375 + x = -3.897615457 Solving -0.4375 + x = -3.897615457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -3.897615457 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -3.897615457 + 0.4375 x = -3.897615457 + 0.4375 Combine like terms: -3.897615457 + 0.4375 = -3.460115457 x = -3.460115457 Simplifying x = -3.460115457Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.335115457, -3.460115457}
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