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Simplifying 5x2 + 30x + 36 = 0 Reorder the terms: 36 + 30x + 5x2 = 0 Solving 36 + 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'. 7.2 + 6x + x2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + 6x + -7.2 + x2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + 6x + x2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + 6x + x2 = 0 + -7.2 6x + x2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 6x + x2 = -7.2 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 = -7.2 + 9 Reorder the terms: 9 + 6x + x2 = -7.2 + 9 Combine like terms: -7.2 + 9 = 1.8 9 + 6x + x2 = 1.8 Factor a perfect square on the left side: (x + 3)(x + 3) = 1.8 Calculate the square root of the right side: 1.341640787 Break this problem into two subproblems by setting (x + 3) equal to 1.341640787 and -1.341640787.Subproblem 1
x + 3 = 1.341640787 Simplifying x + 3 = 1.341640787 Reorder the terms: 3 + x = 1.341640787 Solving 3 + x = 1.341640787 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 = 1.341640787 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.341640787 + -3 x = 1.341640787 + -3 Combine like terms: 1.341640787 + -3 = -1.658359213 x = -1.658359213 Simplifying x = -1.658359213Subproblem 2
x + 3 = -1.341640787 Simplifying x + 3 = -1.341640787 Reorder the terms: 3 + x = -1.341640787 Solving 3 + x = -1.341640787 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 = -1.341640787 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.341640787 + -3 x = -1.341640787 + -3 Combine like terms: -1.341640787 + -3 = -4.341640787 x = -4.341640787 Simplifying x = -4.341640787Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.658359213, -4.341640787}
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