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Simplifying 8x2 + 30x + -19 = 0 Reorder the terms: -19 + 30x + 8x2 = 0 Solving -19 + 30x + 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'. -2.375 + 3.75x + x2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + 3.75x + 2.375 + x2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + 3.75x + x2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + 3.75x + x2 = 0 + 2.375 3.75x + x2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 3.75x + x2 = 2.375 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 2.375 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 2.375 + 3.515625 Combine like terms: 2.375 + 3.515625 = 5.890625 3.515625 + 3.75x + x2 = 5.890625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 5.890625 Calculate the square root of the right side: 2.42706098 Break this problem into two subproblems by setting (x + 1.875) equal to 2.42706098 and -2.42706098.Subproblem 1
x + 1.875 = 2.42706098 Simplifying x + 1.875 = 2.42706098 Reorder the terms: 1.875 + x = 2.42706098 Solving 1.875 + x = 2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 2.42706098 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 2.42706098 + -1.875 x = 2.42706098 + -1.875 Combine like terms: 2.42706098 + -1.875 = 0.55206098 x = 0.55206098 Simplifying x = 0.55206098Subproblem 2
x + 1.875 = -2.42706098 Simplifying x + 1.875 = -2.42706098 Reorder the terms: 1.875 + x = -2.42706098 Solving 1.875 + x = -2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -2.42706098 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -2.42706098 + -1.875 x = -2.42706098 + -1.875 Combine like terms: -2.42706098 + -1.875 = -4.30206098 x = -4.30206098 Simplifying x = -4.30206098Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.55206098, -4.30206098}
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