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Simplifying 8x2 + -15x + -33 = 0 Reorder the terms: -33 + -15x + 8x2 = 0 Solving -33 + -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'. -4.125 + -1.875x + x2 = 0 Move the constant term to the right: Add '4.125' to each side of the equation. -4.125 + -1.875x + 4.125 + x2 = 0 + 4.125 Reorder the terms: -4.125 + 4.125 + -1.875x + x2 = 0 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + -1.875x + x2 = 0 + 4.125 -1.875x + x2 = 0 + 4.125 Combine like terms: 0 + 4.125 = 4.125 -1.875x + x2 = 4.125 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 = 4.125 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 4.125 + 0.87890625 Combine like terms: 4.125 + 0.87890625 = 5.00390625 0.87890625 + -1.875x + x2 = 5.00390625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 5.00390625 Calculate the square root of the right side: 2.236941271 Break this problem into two subproblems by setting (x + -0.9375) equal to 2.236941271 and -2.236941271.Subproblem 1
x + -0.9375 = 2.236941271 Simplifying x + -0.9375 = 2.236941271 Reorder the terms: -0.9375 + x = 2.236941271 Solving -0.9375 + x = 2.236941271 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 = 2.236941271 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 2.236941271 + 0.9375 x = 2.236941271 + 0.9375 Combine like terms: 2.236941271 + 0.9375 = 3.174441271 x = 3.174441271 Simplifying x = 3.174441271Subproblem 2
x + -0.9375 = -2.236941271 Simplifying x + -0.9375 = -2.236941271 Reorder the terms: -0.9375 + x = -2.236941271 Solving -0.9375 + x = -2.236941271 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 = -2.236941271 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -2.236941271 + 0.9375 x = -2.236941271 + 0.9375 Combine like terms: -2.236941271 + 0.9375 = -1.299441271 x = -1.299441271 Simplifying x = -1.299441271Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.174441271, -1.299441271}
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