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Simplifying 10x2 + 30x + 9 = 0 Reorder the terms: 9 + 30x + 10x2 = 0 Solving 9 + 30x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.9 + 3x + x2 = 0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + 3x + -0.9 + x2 = 0 + -0.9 Reorder the terms: 0.9 + -0.9 + 3x + x2 = 0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + 3x + x2 = 0 + -0.9 3x + x2 = 0 + -0.9 Combine like terms: 0 + -0.9 = -0.9 3x + x2 = -0.9 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -0.9 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -0.9 + 2.25 Combine like terms: -0.9 + 2.25 = 1.35 2.25 + 3x + x2 = 1.35 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.35 Calculate the square root of the right side: 1.161895004 Break this problem into two subproblems by setting (x + 1.5) equal to 1.161895004 and -1.161895004.Subproblem 1
x + 1.5 = 1.161895004 Simplifying x + 1.5 = 1.161895004 Reorder the terms: 1.5 + x = 1.161895004 Solving 1.5 + x = 1.161895004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.161895004 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.161895004 + -1.5 x = 1.161895004 + -1.5 Combine like terms: 1.161895004 + -1.5 = -0.338104996 x = -0.338104996 Simplifying x = -0.338104996Subproblem 2
x + 1.5 = -1.161895004 Simplifying x + 1.5 = -1.161895004 Reorder the terms: 1.5 + x = -1.161895004 Solving 1.5 + x = -1.161895004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.161895004 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.161895004 + -1.5 x = -1.161895004 + -1.5 Combine like terms: -1.161895004 + -1.5 = -2.661895004 x = -2.661895004 Simplifying x = -2.661895004Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.338104996, -2.661895004}
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