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Simplifying x * 5(x + 3) = 27 Reorder the terms: x * 5(3 + x) = 27 Reorder the terms for easier multiplication: 5x(3 + x) = 27 (3 * 5x + x * 5x) = 27 (15x + 5x2) = 27 Solving 15x + 5x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 15x + 5x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.4 + 3x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 3x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 3x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 3x + x2 = 0 + 5.4 3x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 3x + x2 = 5.4 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 5.4 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 5.4 + 2.25 Combine like terms: 5.4 + 2.25 = 7.65 2.25 + 3x + x2 = 7.65 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 7.65 Calculate the square root of the right side: 2.765863337 Break this problem into two subproblems by setting (x + 1.5) equal to 2.765863337 and -2.765863337.Subproblem 1
x + 1.5 = 2.765863337 Simplifying x + 1.5 = 2.765863337 Reorder the terms: 1.5 + x = 2.765863337 Solving 1.5 + x = 2.765863337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.765863337 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.765863337 + -1.5 x = 2.765863337 + -1.5 Combine like terms: 2.765863337 + -1.5 = 1.265863337 x = 1.265863337 Simplifying x = 1.265863337Subproblem 2
x + 1.5 = -2.765863337 Simplifying x + 1.5 = -2.765863337 Reorder the terms: 1.5 + x = -2.765863337 Solving 1.5 + x = -2.765863337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.765863337 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.765863337 + -1.5 x = -2.765863337 + -1.5 Combine like terms: -2.765863337 + -1.5 = -4.265863337 x = -4.265863337 Simplifying x = -4.265863337Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.265863337, -4.265863337}
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