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Simplifying 3x2 + 15x + -6.9 = 0 Reorder the terms: -6.9 + 15x + 3x2 = 0 Solving -6.9 + 15x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.3 + 5x + x2 = 0 Move the constant term to the right: Add '2.3' to each side of the equation. -2.3 + 5x + 2.3 + x2 = 0 + 2.3 Reorder the terms: -2.3 + 2.3 + 5x + x2 = 0 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + 5x + x2 = 0 + 2.3 5x + x2 = 0 + 2.3 Combine like terms: 0 + 2.3 = 2.3 5x + x2 = 2.3 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 2.3 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 2.3 + 6.25 Combine like terms: 2.3 + 6.25 = 8.55 6.25 + 5x + x2 = 8.55 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 8.55 Calculate the square root of the right side: 2.924038303 Break this problem into two subproblems by setting (x + 2.5) equal to 2.924038303 and -2.924038303.Subproblem 1
x + 2.5 = 2.924038303 Simplifying x + 2.5 = 2.924038303 Reorder the terms: 2.5 + x = 2.924038303 Solving 2.5 + x = 2.924038303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.924038303 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.924038303 + -2.5 x = 2.924038303 + -2.5 Combine like terms: 2.924038303 + -2.5 = 0.424038303 x = 0.424038303 Simplifying x = 0.424038303Subproblem 2
x + 2.5 = -2.924038303 Simplifying x + 2.5 = -2.924038303 Reorder the terms: 2.5 + x = -2.924038303 Solving 2.5 + x = -2.924038303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.924038303 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.924038303 + -2.5 x = -2.924038303 + -2.5 Combine like terms: -2.924038303 + -2.5 = -5.424038303 x = -5.424038303 Simplifying x = -5.424038303Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.424038303, -5.424038303}
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