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Simplifying 4x2 = 27x + -40 + 0 Reorder the terms: 4x2 = -40 + 0 + 27x Combine like terms: -40 + 0 = -40 4x2 = -40 + 27x Solving 4x2 = -40 + 27x Solving for variable 'x'. Reorder the terms: 40 + -27x + 4x2 = -40 + 27x + 40 + -27x Reorder the terms: 40 + -27x + 4x2 = -40 + 40 + 27x + -27x Combine like terms: -40 + 40 = 0 40 + -27x + 4x2 = 0 + 27x + -27x 40 + -27x + 4x2 = 27x + -27x Combine like terms: 27x + -27x = 0 40 + -27x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 10 + -6.75x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -6.75x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -6.75x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -6.75x + x2 = 0 + -10 -6.75x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -6.75x + x2 = -10 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 = -10 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = -10 + 11.390625 Combine like terms: -10 + 11.390625 = 1.390625 11.390625 + -6.75x + x2 = 1.390625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x + -3.375) equal to 1.179247642 and -1.179247642.Subproblem 1
x + -3.375 = 1.179247642 Simplifying x + -3.375 = 1.179247642 Reorder the terms: -3.375 + x = 1.179247642 Solving -3.375 + x = 1.179247642 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 = 1.179247642 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 1.179247642 + 3.375 x = 1.179247642 + 3.375 Combine like terms: 1.179247642 + 3.375 = 4.554247642 x = 4.554247642 Simplifying x = 4.554247642Subproblem 2
x + -3.375 = -1.179247642 Simplifying x + -3.375 = -1.179247642 Reorder the terms: -3.375 + x = -1.179247642 Solving -3.375 + x = -1.179247642 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 = -1.179247642 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -1.179247642 + 3.375 x = -1.179247642 + 3.375 Combine like terms: -1.179247642 + 3.375 = 2.195752358 x = 2.195752358 Simplifying x = 2.195752358Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.554247642, 2.195752358}
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