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Simplifying 3(x * x) + 45x + 20.25 = 0 Multiply x * x 3(x2) + 45x + 20.25 = 0 Reorder the terms: 20.25 + 45x + 3x2 = 0 Solving 20.25 + 45x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 6.75 + 15x + x2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + 15x + -6.75 + x2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + 15x + x2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + 15x + x2 = 0 + -6.75 15x + x2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 15x + x2 = -6.75 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 = -6.75 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -6.75 + 56.25 Combine like terms: -6.75 + 56.25 = 49.5 56.25 + 15x + x2 = 49.5 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 49.5 Calculate the square root of the right side: 7.03562364 Break this problem into two subproblems by setting (x + 7.5) equal to 7.03562364 and -7.03562364.Subproblem 1
x + 7.5 = 7.03562364 Simplifying x + 7.5 = 7.03562364 Reorder the terms: 7.5 + x = 7.03562364 Solving 7.5 + x = 7.03562364 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 = 7.03562364 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.03562364 + -7.5 x = 7.03562364 + -7.5 Combine like terms: 7.03562364 + -7.5 = -0.46437636 x = -0.46437636 Simplifying x = -0.46437636Subproblem 2
x + 7.5 = -7.03562364 Simplifying x + 7.5 = -7.03562364 Reorder the terms: 7.5 + x = -7.03562364 Solving 7.5 + x = -7.03562364 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 = -7.03562364 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.03562364 + -7.5 x = -7.03562364 + -7.5 Combine like terms: -7.03562364 + -7.5 = -14.53562364 x = -14.53562364 Simplifying x = -14.53562364Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.46437636, -14.53562364}
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