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Simplifying 2x2 + 30x + 45 = 0 Reorder the terms: 45 + 30x + 2x2 = 0 Solving 45 + 30x + 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'. 22.5 + 15x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + 15x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + 15x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + 15x + x2 = 0 + -22.5 15x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 15x + x2 = -22.5 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -22.5 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -22.5 + 56.25 Combine like terms: -22.5 + 56.25 = 33.75 56.25 + 15x + x2 = 33.75 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 33.75 Calculate the square root of the right side: 5.809475019 Break this problem into two subproblems by setting (x + 7.5) equal to 5.809475019 and -5.809475019.Subproblem 1
x + 7.5 = 5.809475019 Simplifying x + 7.5 = 5.809475019 Reorder the terms: 7.5 + x = 5.809475019 Solving 7.5 + x = 5.809475019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 5.809475019 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 5.809475019 + -7.5 x = 5.809475019 + -7.5 Combine like terms: 5.809475019 + -7.5 = -1.690524981 x = -1.690524981 Simplifying x = -1.690524981Subproblem 2
x + 7.5 = -5.809475019 Simplifying x + 7.5 = -5.809475019 Reorder the terms: 7.5 + x = -5.809475019 Solving 7.5 + x = -5.809475019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -5.809475019 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -5.809475019 + -7.5 x = -5.809475019 + -7.5 Combine like terms: -5.809475019 + -7.5 = -13.309475019 x = -13.309475019 Simplifying x = -13.309475019Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.690524981, -13.309475019}
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