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Simplifying 18 + -3x + -2x2 = 0 Solving 18 + -3x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -9 + 1.5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 1.5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 1.5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 1.5x + x2 = 0 + 9 1.5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 1.5x + x2 = 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 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 9 + 0.5625 Combine like terms: 9 + 0.5625 = 9.5625 0.5625 + 1.5x + x2 = 9.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (x + 0.75) equal to 3.092329219 and -3.092329219.Subproblem 1
x + 0.75 = 3.092329219 Simplifying x + 0.75 = 3.092329219 Reorder the terms: 0.75 + x = 3.092329219 Solving 0.75 + x = 3.092329219 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 = 3.092329219 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 3.092329219 + -0.75 x = 3.092329219 + -0.75 Combine like terms: 3.092329219 + -0.75 = 2.342329219 x = 2.342329219 Simplifying x = 2.342329219Subproblem 2
x + 0.75 = -3.092329219 Simplifying x + 0.75 = -3.092329219 Reorder the terms: 0.75 + x = -3.092329219 Solving 0.75 + x = -3.092329219 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 = -3.092329219 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -3.092329219 + -0.75 x = -3.092329219 + -0.75 Combine like terms: -3.092329219 + -0.75 = -3.842329219 x = -3.842329219 Simplifying x = -3.842329219Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.342329219, -3.842329219}
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