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Simplifying 5x2 + 15x + -6 = 0 Reorder the terms: -6 + 15x + 5x2 = 0 Solving -6 + 15x + 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'. -1.2 + 3x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 3x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 3x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 3x + x2 = 0 + 1.2 3x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 3x + x2 = 1.2 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 1.2 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1.2 + 2.25 Combine like terms: 1.2 + 2.25 = 3.45 2.25 + 3x + x2 = 3.45 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.45 Calculate the square root of the right side: 1.857417562 Break this problem into two subproblems by setting (x + 1.5) equal to 1.857417562 and -1.857417562.Subproblem 1
x + 1.5 = 1.857417562 Simplifying x + 1.5 = 1.857417562 Reorder the terms: 1.5 + x = 1.857417562 Solving 1.5 + x = 1.857417562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.857417562 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.857417562 + -1.5 x = 1.857417562 + -1.5 Combine like terms: 1.857417562 + -1.5 = 0.357417562 x = 0.357417562 Simplifying x = 0.357417562Subproblem 2
x + 1.5 = -1.857417562 Simplifying x + 1.5 = -1.857417562 Reorder the terms: 1.5 + x = -1.857417562 Solving 1.5 + x = -1.857417562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.857417562 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.857417562 + -1.5 x = -1.857417562 + -1.5 Combine like terms: -1.857417562 + -1.5 = -3.357417562 x = -3.357417562 Simplifying x = -3.357417562Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.357417562, -3.357417562}
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