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Simplifying x(2x + 3) = 19.8 Reorder the terms: x(3 + 2x) = 19.8 (3 * x + 2x * x) = 19.8 (3x + 2x2) = 19.8 Solving 3x + 2x2 = 19.8 Solving for variable 'x'. Reorder the terms: -19.8 + 3x + 2x2 = 19.8 + -19.8 Combine like terms: 19.8 + -19.8 = 0.0 -19.8 + 3x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.9 + 1.5x + x2 = 0.0 Move the constant term to the right: Add '9.9' to each side of the equation. -9.9 + 1.5x + 9.9 + x2 = 0.0 + 9.9 Reorder the terms: -9.9 + 9.9 + 1.5x + x2 = 0.0 + 9.9 Combine like terms: -9.9 + 9.9 = 0.0 0.0 + 1.5x + x2 = 0.0 + 9.9 1.5x + x2 = 0.0 + 9.9 Combine like terms: 0.0 + 9.9 = 9.9 1.5x + x2 = 9.9 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 = 9.9 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 9.9 + 0.5625 Combine like terms: 9.9 + 0.5625 = 10.4625 0.5625 + 1.5x + x2 = 10.4625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 10.4625 Calculate the square root of the right side: 3.234578798 Break this problem into two subproblems by setting (x + 0.75) equal to 3.234578798 and -3.234578798.Subproblem 1
x + 0.75 = 3.234578798 Simplifying x + 0.75 = 3.234578798 Reorder the terms: 0.75 + x = 3.234578798 Solving 0.75 + x = 3.234578798 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 = 3.234578798 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 3.234578798 + -0.75 x = 3.234578798 + -0.75 Combine like terms: 3.234578798 + -0.75 = 2.484578798 x = 2.484578798 Simplifying x = 2.484578798Subproblem 2
x + 0.75 = -3.234578798 Simplifying x + 0.75 = -3.234578798 Reorder the terms: 0.75 + x = -3.234578798 Solving 0.75 + x = -3.234578798 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 = -3.234578798 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -3.234578798 + -0.75 x = -3.234578798 + -0.75 Combine like terms: -3.234578798 + -0.75 = -3.984578798 x = -3.984578798 Simplifying x = -3.984578798Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.484578798, -3.984578798}
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