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Simplifying 1.5x2 + -15x + -35 = 0 Reorder the terms: -35 + -15x + 1.5x2 = 0 Solving -35 + -15x + 1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -23.33333333 + -10x + x2 = 0 Move the constant term to the right: Add '23.33333333' to each side of the equation. -23.33333333 + -10x + 23.33333333 + x2 = 0 + 23.33333333 Reorder the terms: -23.33333333 + 23.33333333 + -10x + x2 = 0 + 23.33333333 Combine like terms: -23.33333333 + 23.33333333 = 0.00000000 0.00000000 + -10x + x2 = 0 + 23.33333333 -10x + x2 = 0 + 23.33333333 Combine like terms: 0 + 23.33333333 = 23.33333333 -10x + x2 = 23.33333333 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 23.33333333 + 25 Reorder the terms: 25 + -10x + x2 = 23.33333333 + 25 Combine like terms: 23.33333333 + 25 = 48.33333333 25 + -10x + x2 = 48.33333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 48.33333333 Calculate the square root of the right side: 6.952217871 Break this problem into two subproblems by setting (x + -5) equal to 6.952217871 and -6.952217871.Subproblem 1
x + -5 = 6.952217871 Simplifying x + -5 = 6.952217871 Reorder the terms: -5 + x = 6.952217871 Solving -5 + x = 6.952217871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 6.952217871 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.952217871 + 5 x = 6.952217871 + 5 Combine like terms: 6.952217871 + 5 = 11.952217871 x = 11.952217871 Simplifying x = 11.952217871Subproblem 2
x + -5 = -6.952217871 Simplifying x + -5 = -6.952217871 Reorder the terms: -5 + x = -6.952217871 Solving -5 + x = -6.952217871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -6.952217871 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.952217871 + 5 x = -6.952217871 + 5 Combine like terms: -6.952217871 + 5 = -1.952217871 x = -1.952217871 Simplifying x = -1.952217871Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.952217871, -1.952217871}
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