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Simplifying 3x2 + -15x + -70 = 0 Reorder the terms: -70 + -15x + 3x2 = 0 Solving -70 + -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'. -23.33333333 + -5x + x2 = 0 Move the constant term to the right: Add '23.33333333' to each side of the equation. -23.33333333 + -5x + 23.33333333 + x2 = 0 + 23.33333333 Reorder the terms: -23.33333333 + 23.33333333 + -5x + x2 = 0 + 23.33333333 Combine like terms: -23.33333333 + 23.33333333 = 0.00000000 0.00000000 + -5x + x2 = 0 + 23.33333333 -5x + x2 = 0 + 23.33333333 Combine like terms: 0 + 23.33333333 = 23.33333333 -5x + x2 = 23.33333333 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 = 23.33333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 23.33333333 + 6.25 Combine like terms: 23.33333333 + 6.25 = 29.58333333 6.25 + -5x + x2 = 29.58333333 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 29.58333333 Calculate the square root of the right side: 5.43905629 Break this problem into two subproblems by setting (x + -2.5) equal to 5.43905629 and -5.43905629.Subproblem 1
x + -2.5 = 5.43905629 Simplifying x + -2.5 = 5.43905629 Reorder the terms: -2.5 + x = 5.43905629 Solving -2.5 + x = 5.43905629 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 = 5.43905629 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.43905629 + 2.5 x = 5.43905629 + 2.5 Combine like terms: 5.43905629 + 2.5 = 7.93905629 x = 7.93905629 Simplifying x = 7.93905629Subproblem 2
x + -2.5 = -5.43905629 Simplifying x + -2.5 = -5.43905629 Reorder the terms: -2.5 + x = -5.43905629 Solving -2.5 + x = -5.43905629 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 = -5.43905629 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.43905629 + 2.5 x = -5.43905629 + 2.5 Combine like terms: -5.43905629 + 2.5 = -2.93905629 x = -2.93905629 Simplifying x = -2.93905629Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.93905629, -2.93905629}
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