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Simplifying 5x2 + 5x + -9 = 9 Reorder the terms: -9 + 5x + 5x2 = 9 Solving -9 + 5x + 5x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -9 + 5x + 5x2 = 9 + -9 Combine like terms: -9 + -9 = -18 -18 + 5x + 5x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -18 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x + x2 = 0 + 3.6 x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 x + x2 = 3.6 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 3.6 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 3.6 + 0.25 Combine like terms: 3.6 + 0.25 = 3.85 1.25 + x2 = 3.85 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.85 Calculate the square root of the right side: 1.962141687 Break this problem into two subproblems by setting (x + 0.5) equal to 1.962141687 and -1.962141687.Subproblem 1
x + 0.5 = 1.962141687 Simplifying x + 0.5 = 1.962141687 Reorder the terms: 0.5 + x = 1.962141687 Solving 0.5 + x = 1.962141687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.962141687 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.962141687 + -0.5 x = 1.962141687 + -0.5 Combine like terms: 1.962141687 + -0.5 = 1.462141687 x = 1.462141687 Simplifying x = 1.462141687Subproblem 2
x + 0.5 = -1.962141687 Simplifying x + 0.5 = -1.962141687 Reorder the terms: 0.5 + x = -1.962141687 Solving 0.5 + x = -1.962141687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.962141687 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.962141687 + -0.5 x = -1.962141687 + -0.5 Combine like terms: -1.962141687 + -0.5 = -2.462141687 x = -2.462141687 Simplifying x = -2.462141687Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.462141687, -2.462141687}
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