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Simplifying -17 + 30x + 5x2 = 0 Solving -17 + 30x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + 6x + x2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + 6x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + 6x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + 6x + x2 = 0 + 3.4 6x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 6x + x2 = 3.4 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 3.4 + 9 Reorder the terms: 9 + 6x + x2 = 3.4 + 9 Combine like terms: 3.4 + 9 = 12.4 9 + 6x + x2 = 12.4 Factor a perfect square on the left side: (x + 3)(x + 3) = 12.4 Calculate the square root of the right side: 3.521363372 Break this problem into two subproblems by setting (x + 3) equal to 3.521363372 and -3.521363372.Subproblem 1
x + 3 = 3.521363372 Simplifying x + 3 = 3.521363372 Reorder the terms: 3 + x = 3.521363372 Solving 3 + x = 3.521363372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.521363372 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.521363372 + -3 x = 3.521363372 + -3 Combine like terms: 3.521363372 + -3 = 0.521363372 x = 0.521363372 Simplifying x = 0.521363372Subproblem 2
x + 3 = -3.521363372 Simplifying x + 3 = -3.521363372 Reorder the terms: 3 + x = -3.521363372 Solving 3 + x = -3.521363372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.521363372 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.521363372 + -3 x = -3.521363372 + -3 Combine like terms: -3.521363372 + -3 = -6.521363372 x = -6.521363372 Simplifying x = -6.521363372Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.521363372, -6.521363372}
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