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Simplifying (2x + -9)(2x + -9) + 5x(4 + -3) = 999999999999999 Reorder the terms: (-9 + 2x)(2x + -9) + 5x(4 + -3) = 999999999999999 Reorder the terms: (-9 + 2x)(-9 + 2x) + 5x(4 + -3) = 999999999999999 Multiply (-9 + 2x) * (-9 + 2x) (-9(-9 + 2x) + 2x * (-9 + 2x)) + 5x(4 + -3) = 999999999999999 ((-9 * -9 + 2x * -9) + 2x * (-9 + 2x)) + 5x(4 + -3) = 999999999999999 ((81 + -18x) + 2x * (-9 + 2x)) + 5x(4 + -3) = 999999999999999 (81 + -18x + (-9 * 2x + 2x * 2x)) + 5x(4 + -3) = 999999999999999 (81 + -18x + (-18x + 4x2)) + 5x(4 + -3) = 999999999999999 Combine like terms: -18x + -18x = -36x (81 + -36x + 4x2) + 5x(4 + -3) = 999999999999999 Combine like terms: 4 + -3 = 1 81 + -36x + 4x2 + 5x(1) = 999999999999999 Reorder the terms for easier multiplication: 81 + -36x + 4x2 + 5 * 1x = 999999999999999 Multiply 5 * 1 81 + -36x + 4x2 + 5x = 999999999999999 Reorder the terms: 81 + -36x + 5x + 4x2 = 999999999999999 Combine like terms: -36x + 5x = -31x 81 + -31x + 4x2 = 999999999999999 Solving 81 + -31x + 4x2 = 999999999999999 Solving for variable 'x'. Reorder the terms: 81 + -999999999999999 + -31x + 4x2 = 999999999999999 + -999999999999999 Combine like terms: 81 + -999999999999999 = -999999999999918 -999999999999918 + -31x + 4x2 = 999999999999999 + -999999999999999 Combine like terms: 999999999999999 + -999999999999999 = 0 -999999999999918 + -31x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -250000000000000 + -7.75x + x2 = 0 Move the constant term to the right: Add '250000000000000' to each side of the equation. -250000000000000 + -7.75x + 250000000000000 + x2 = 0 + 250000000000000 Reorder the terms: -250000000000000 + 250000000000000 + -7.75x + x2 = 0 + 250000000000000 Combine like terms: -250000000000000 + 250000000000000 = 0 0 + -7.75x + x2 = 0 + 250000000000000 -7.75x + x2 = 0 + 250000000000000 Combine like terms: 0 + 250000000000000 = 250000000000000 -7.75x + x2 = 250000000000000 The x term is -7.75x. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75x + 15.015625 + x2 = 250000000000000 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = 250000000000000 + 15.015625 Combine like terms: 250000000000000 + 15.015625 = 250000000000015.015625 15.015625 + -7.75x + x2 = 250000000000015.015625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 250000000000015.015625 Calculate the square root of the right side: 15811388.300842371 Break this problem into two subproblems by setting (x + -3.875) equal to 15811388.300842371 and -15811388.300842371.Subproblem 1
x + -3.875 = 15811388.300842371 Simplifying x + -3.875 = 15811388.300842371 Reorder the terms: -3.875 + x = 15811388.300842371 Solving -3.875 + x = 15811388.300842371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = 15811388.300842371 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 15811388.300842371 + 3.875 x = 15811388.300842371 + 3.875 Combine like terms: 15811388.300842371 + 3.875 = 15811392.175842371 x = 15811392.175842371 Simplifying x = 15811392.175842371Subproblem 2
x + -3.875 = -15811388.300842371 Simplifying x + -3.875 = -15811388.300842371 Reorder the terms: -3.875 + x = -15811388.300842371 Solving -3.875 + x = -15811388.300842371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = -15811388.300842371 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -15811388.300842371 + 3.875 x = -15811388.300842371 + 3.875 Combine like terms: -15811388.300842371 + 3.875 = -15811384.425842371 x = -15811384.425842371 Simplifying x = -15811384.425842371Solution
The solution to the problem is based on the solutions from the subproblems. x = {15811392.175842371, -15811384.425842371}
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