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Simplifying 0 = -5x2 + -30x + 2 Reorder the terms: 0 = 2 + -30x + -5x2 Solving 0 = 2 + -30x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + 30x + 5x2 = 2 + -30x + -5x2 + -2 + 30x + 5x2 Reorder the terms: -2 + 30x + 5x2 = 2 + -2 + -30x + 30x + -5x2 + 5x2 Combine like terms: 2 + -2 = 0 -2 + 30x + 5x2 = 0 + -30x + 30x + -5x2 + 5x2 -2 + 30x + 5x2 = -30x + 30x + -5x2 + 5x2 Combine like terms: -30x + 30x = 0 -2 + 30x + 5x2 = 0 + -5x2 + 5x2 -2 + 30x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -2 + 30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 6x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 6x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 6x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 6x + x2 = 0 + 0.4 6x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 6x + x2 = 0.4 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 = 0.4 + 9 Reorder the terms: 9 + 6x + x2 = 0.4 + 9 Combine like terms: 0.4 + 9 = 9.4 9 + 6x + x2 = 9.4 Factor a perfect square on the left side: (x + 3)(x + 3) = 9.4 Calculate the square root of the right side: 3.065941943 Break this problem into two subproblems by setting (x + 3) equal to 3.065941943 and -3.065941943.Subproblem 1
x + 3 = 3.065941943 Simplifying x + 3 = 3.065941943 Reorder the terms: 3 + x = 3.065941943 Solving 3 + x = 3.065941943 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 = 3.065941943 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.065941943 + -3 x = 3.065941943 + -3 Combine like terms: 3.065941943 + -3 = 0.065941943 x = 0.065941943 Simplifying x = 0.065941943Subproblem 2
x + 3 = -3.065941943 Simplifying x + 3 = -3.065941943 Reorder the terms: 3 + x = -3.065941943 Solving 3 + x = -3.065941943 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 = -3.065941943 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.065941943 + -3 x = -3.065941943 + -3 Combine like terms: -3.065941943 + -3 = -6.065941943 x = -6.065941943 Simplifying x = -6.065941943Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.065941943, -6.065941943}
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