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Simplifying 8x2 + 15x + 6 = 0 Reorder the terms: 6 + 15x + 8x2 = 0 Solving 6 + 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'. 0.75 + 1.875x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 1.875x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 1.875x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 1.875x + x2 = 0 + -0.75 1.875x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 1.875x + x2 = -0.75 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 = -0.75 + 0.87890625 Reorder the terms: 0.87890625 + 1.875x + x2 = -0.75 + 0.87890625 Combine like terms: -0.75 + 0.87890625 = 0.12890625 0.87890625 + 1.875x + x2 = 0.12890625 Factor a perfect square on the left side: (x + 0.9375)(x + 0.9375) = 0.12890625 Calculate the square root of the right side: 0.359035165 Break this problem into two subproblems by setting (x + 0.9375) equal to 0.359035165 and -0.359035165.Subproblem 1
x + 0.9375 = 0.359035165 Simplifying x + 0.9375 = 0.359035165 Reorder the terms: 0.9375 + x = 0.359035165 Solving 0.9375 + x = 0.359035165 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 = 0.359035165 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = 0.359035165 + -0.9375 x = 0.359035165 + -0.9375 Combine like terms: 0.359035165 + -0.9375 = -0.578464835 x = -0.578464835 Simplifying x = -0.578464835Subproblem 2
x + 0.9375 = -0.359035165 Simplifying x + 0.9375 = -0.359035165 Reorder the terms: 0.9375 + x = -0.359035165 Solving 0.9375 + x = -0.359035165 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 = -0.359035165 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = -0.359035165 + -0.9375 x = -0.359035165 + -0.9375 Combine like terms: -0.359035165 + -0.9375 = -1.296535165 x = -1.296535165 Simplifying x = -1.296535165Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.578464835, -1.296535165}
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