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Simplifying 0.1x2 + 0.7x + 1 = 0 Reorder the terms: 1 + 0.7x + 0.1x2 = 0 Solving 1 + 0.7x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 10 + 7x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 7x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 7x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 7x + x2 = 0 + -10 7x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 7x + x2 = -10 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -10 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -10 + 12.25 Combine like terms: -10 + 12.25 = 2.25 12.25 + 7x + x2 = 2.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + 3.5) equal to 1.5 and -1.5.Subproblem 1
x + 3.5 = 1.5 Simplifying x + 3.5 = 1.5 Reorder the terms: 3.5 + x = 1.5 Solving 3.5 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 1.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 1.5 + -3.5 x = 1.5 + -3.5 Combine like terms: 1.5 + -3.5 = -2 x = -2 Simplifying x = -2Subproblem 2
x + 3.5 = -1.5 Simplifying x + 3.5 = -1.5 Reorder the terms: 3.5 + x = -1.5 Solving 3.5 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -1.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -1.5 + -3.5 x = -1.5 + -3.5 Combine like terms: -1.5 + -3.5 = -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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