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Simplifying 2x(4x + 5) = 27 Reorder the terms: 2x(5 + 4x) = 27 (5 * 2x + 4x * 2x) = 27 (10x + 8x2) = 27 Solving 10x + 8x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 10x + 8x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 10x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.375 + 1.25x + x2 = 0 Move the constant term to the right: Add '3.375' to each side of the equation. -3.375 + 1.25x + 3.375 + x2 = 0 + 3.375 Reorder the terms: -3.375 + 3.375 + 1.25x + x2 = 0 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + 1.25x + x2 = 0 + 3.375 1.25x + x2 = 0 + 3.375 Combine like terms: 0 + 3.375 = 3.375 1.25x + x2 = 3.375 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 3.375 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 3.375 + 0.390625 Combine like terms: 3.375 + 0.390625 = 3.765625 0.390625 + 1.25x + x2 = 3.765625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (x + 0.625) equal to 1.940521837 and -1.940521837.Subproblem 1
x + 0.625 = 1.940521837 Simplifying x + 0.625 = 1.940521837 Reorder the terms: 0.625 + x = 1.940521837 Solving 0.625 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.940521837 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.940521837 + -0.625 x = 1.940521837 + -0.625 Combine like terms: 1.940521837 + -0.625 = 1.315521837 x = 1.315521837 Simplifying x = 1.315521837Subproblem 2
x + 0.625 = -1.940521837 Simplifying x + 0.625 = -1.940521837 Reorder the terms: 0.625 + x = -1.940521837 Solving 0.625 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.940521837 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.940521837 + -0.625 x = -1.940521837 + -0.625 Combine like terms: -1.940521837 + -0.625 = -2.565521837 x = -2.565521837 Simplifying x = -2.565521837Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.315521837, -2.565521837}
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