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Simplifying -5x2 + -18x + -2 = 0 Reorder the terms: -2 + -18x + -5x2 = 0 Solving -2 + -18x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 18x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 18x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + 18x + 5x2 = 0 Solving 2 + 18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 3.6x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 3.6x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 3.6x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 3.6x + x2 = 0 + -0.4 3.6x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 3.6x + x2 = -0.4 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = -0.4 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = -0.4 + 3.24 Combine like terms: -0.4 + 3.24 = 2.84 3.24 + 3.6x + x2 = 2.84 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 2.84 Calculate the square root of the right side: 1.685229955 Break this problem into two subproblems by setting (x + 1.8) equal to 1.685229955 and -1.685229955.Subproblem 1
x + 1.8 = 1.685229955 Simplifying x + 1.8 = 1.685229955 Reorder the terms: 1.8 + x = 1.685229955 Solving 1.8 + x = 1.685229955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 1.685229955 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 1.685229955 + -1.8 x = 1.685229955 + -1.8 Combine like terms: 1.685229955 + -1.8 = -0.114770045 x = -0.114770045 Simplifying x = -0.114770045Subproblem 2
x + 1.8 = -1.685229955 Simplifying x + 1.8 = -1.685229955 Reorder the terms: 1.8 + x = -1.685229955 Solving 1.8 + x = -1.685229955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -1.685229955 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -1.685229955 + -1.8 x = -1.685229955 + -1.8 Combine like terms: -1.685229955 + -1.8 = -3.485229955 x = -3.485229955 Simplifying x = -3.485229955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.114770045, -3.485229955}Solution
x = {-0.114770045, -3.485229955}
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