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Simplifying 4x2 + 27x + -10 = 0 Reorder the terms: -10 + 27x + 4x2 = 0 Solving -10 + 27x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + 6.75x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 6.75x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 6.75x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 6.75x + x2 = 0 + 2.5 6.75x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 6.75x + x2 = 2.5 The x term is 6.75x. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75x + 11.390625 + x2 = 2.5 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = 2.5 + 11.390625 Combine like terms: 2.5 + 11.390625 = 13.890625 11.390625 + 6.75x + x2 = 13.890625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 13.890625 Calculate the square root of the right side: 3.727012879 Break this problem into two subproblems by setting (x + 3.375) equal to 3.727012879 and -3.727012879.Subproblem 1
x + 3.375 = 3.727012879 Simplifying x + 3.375 = 3.727012879 Reorder the terms: 3.375 + x = 3.727012879 Solving 3.375 + x = 3.727012879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = 3.727012879 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 3.727012879 + -3.375 x = 3.727012879 + -3.375 Combine like terms: 3.727012879 + -3.375 = 0.352012879 x = 0.352012879 Simplifying x = 0.352012879Subproblem 2
x + 3.375 = -3.727012879 Simplifying x + 3.375 = -3.727012879 Reorder the terms: 3.375 + x = -3.727012879 Solving 3.375 + x = -3.727012879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = -3.727012879 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -3.727012879 + -3.375 x = -3.727012879 + -3.375 Combine like terms: -3.727012879 + -3.375 = -7.102012879 x = -7.102012879 Simplifying x = -7.102012879Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.352012879, -7.102012879}
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