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Simplifying 5x(2x + 3) = 18 Reorder the terms: 5x(3 + 2x) = 18 (3 * 5x + 2x * 5x) = 18 (15x + 10x2) = 18 Solving 15x + 10x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 15x + 10x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 15x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.8 + 1.5x + x2 = 0.0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 1.5x + 1.8 + x2 = 0.0 + 1.8 Reorder the terms: -1.8 + 1.8 + 1.5x + x2 = 0.0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 1.5x + x2 = 0.0 + 1.8 1.5x + x2 = 0.0 + 1.8 Combine like terms: 0.0 + 1.8 = 1.8 1.5x + x2 = 1.8 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 1.8 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 1.8 + 0.5625 Combine like terms: 1.8 + 0.5625 = 2.3625 0.5625 + 1.5x + x2 = 2.3625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 2.3625 Calculate the square root of the right side: 1.537042615 Break this problem into two subproblems by setting (x + 0.75) equal to 1.537042615 and -1.537042615.Subproblem 1
x + 0.75 = 1.537042615 Simplifying x + 0.75 = 1.537042615 Reorder the terms: 0.75 + x = 1.537042615 Solving 0.75 + x = 1.537042615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.537042615 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.537042615 + -0.75 x = 1.537042615 + -0.75 Combine like terms: 1.537042615 + -0.75 = 0.787042615 x = 0.787042615 Simplifying x = 0.787042615Subproblem 2
x + 0.75 = -1.537042615 Simplifying x + 0.75 = -1.537042615 Reorder the terms: 0.75 + x = -1.537042615 Solving 0.75 + x = -1.537042615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.537042615 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.537042615 + -0.75 x = -1.537042615 + -0.75 Combine like terms: -1.537042615 + -0.75 = -2.287042615 x = -2.287042615 Simplifying x = -2.287042615Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.787042615, -2.287042615}
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