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Simplifying -2x2 + 19x + -18 = 0 Reorder the terms: -18 + 19x + -2x2 = 0 Solving -18 + 19x + -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 + -9.5x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -9.5x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -9.5x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -9.5x + x2 = 0 + -9 -9.5x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -9.5x + x2 = -9 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = -9 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = -9 + 22.5625 Combine like terms: -9 + 22.5625 = 13.5625 22.5625 + -9.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + -4.75) equal to 3.682729966 and -3.682729966.Subproblem 1
x + -4.75 = 3.682729966 Simplifying x + -4.75 = 3.682729966 Reorder the terms: -4.75 + x = 3.682729966 Solving -4.75 + x = 3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 3.682729966 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 3.682729966 + 4.75 x = 3.682729966 + 4.75 Combine like terms: 3.682729966 + 4.75 = 8.432729966 x = 8.432729966 Simplifying x = 8.432729966Subproblem 2
x + -4.75 = -3.682729966 Simplifying x + -4.75 = -3.682729966 Reorder the terms: -4.75 + x = -3.682729966 Solving -4.75 + x = -3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -3.682729966 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -3.682729966 + 4.75 x = -3.682729966 + 4.75 Combine like terms: -3.682729966 + 4.75 = 1.067270034 x = 1.067270034 Simplifying x = 1.067270034Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.432729966, 1.067270034}
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