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Simplifying 0.01x2 + 0.03x + -0.10 = 0 Reorder the terms: -0.10 + 0.03x + 0.01x2 = 0 Solving -0.10 + 0.03x + 0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -10 + 3x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 3x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 3x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 3x + x2 = 0 + 10 3x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 3x + x2 = 10 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 = 10 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 10 + 2.25 Combine like terms: 10 + 2.25 = 12.25 2.25 + 3x + x2 = 12.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 12.25 Calculate the square root of the right side: 3.5 Break this problem into two subproblems by setting (x + 1.5) equal to 3.5 and -3.5.Subproblem 1
x + 1.5 = 3.5 Simplifying x + 1.5 = 3.5 Reorder the terms: 1.5 + x = 3.5 Solving 1.5 + x = 3.5 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 = 3.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.5 + -1.5 x = 3.5 + -1.5 Combine like terms: 3.5 + -1.5 = 2 x = 2 Simplifying x = 2Subproblem 2
x + 1.5 = -3.5 Simplifying x + 1.5 = -3.5 Reorder the terms: 1.5 + x = -3.5 Solving 1.5 + x = -3.5 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 = -3.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.5 + -1.5 x = -3.5 + -1.5 Combine like terms: -3.5 + -1.5 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -5}
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