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Simplifying 0.1x2 + 0.7x = 3 Reorder the terms: 0.7x + 0.1x2 = 3 Solving 0.7x + 0.1x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 0.7x + 0.1x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 0.7x + 0.1x2 = 0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -30 + 7x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 7x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 7x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 7x + x2 = 0 + 30 7x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 7x + x2 = 30 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 = 30 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 30 + 12.25 Combine like terms: 30 + 12.25 = 42.25 12.25 + 7x + x2 = 42.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 42.25 Calculate the square root of the right side: 6.5 Break this problem into two subproblems by setting (x + 3.5) equal to 6.5 and -6.5.Subproblem 1
x + 3.5 = 6.5 Simplifying x + 3.5 = 6.5 Reorder the terms: 3.5 + x = 6.5 Solving 3.5 + x = 6.5 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 = 6.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.5 + -3.5 x = 6.5 + -3.5 Combine like terms: 6.5 + -3.5 = 3 x = 3 Simplifying x = 3Subproblem 2
x + 3.5 = -6.5 Simplifying x + 3.5 = -6.5 Reorder the terms: 3.5 + x = -6.5 Solving 3.5 + x = -6.5 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 = -6.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.5 + -3.5 x = -6.5 + -3.5 Combine like terms: -6.5 + -3.5 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -10}
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