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Simplifying 8x2 + -15x + -24 = 0 Reorder the terms: -24 + -15x + 8x2 = 0 Solving -24 + -15x + 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'. -3 + -1.875x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.875x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -1.875x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.875x + x2 = 0 + 3 -1.875x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.875x + x2 = 3 The x term is -1.875x. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875x + 0.87890625 + x2 = 3 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 3 + 0.87890625 Combine like terms: 3 + 0.87890625 = 3.87890625 0.87890625 + -1.875x + x2 = 3.87890625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 3.87890625 Calculate the square root of the right side: 1.969493907 Break this problem into two subproblems by setting (x + -0.9375) equal to 1.969493907 and -1.969493907.Subproblem 1
x + -0.9375 = 1.969493907 Simplifying x + -0.9375 = 1.969493907 Reorder the terms: -0.9375 + x = 1.969493907 Solving -0.9375 + x = 1.969493907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = 1.969493907 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 1.969493907 + 0.9375 x = 1.969493907 + 0.9375 Combine like terms: 1.969493907 + 0.9375 = 2.906993907 x = 2.906993907 Simplifying x = 2.906993907Subproblem 2
x + -0.9375 = -1.969493907 Simplifying x + -0.9375 = -1.969493907 Reorder the terms: -0.9375 + x = -1.969493907 Solving -0.9375 + x = -1.969493907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = -1.969493907 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -1.969493907 + 0.9375 x = -1.969493907 + 0.9375 Combine like terms: -1.969493907 + 0.9375 = -1.031993907 x = -1.031993907 Simplifying x = -1.031993907Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.906993907, -1.031993907}
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