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Simplifying 0.03x2 + 0.9x + -10 = 2 Reorder the terms: -10 + 0.9x + 0.03x2 = 2 Solving -10 + 0.9x + 0.03x2 = 2 Solving for variable 'x'. Reorder the terms: -10 + -2 + 0.9x + 0.03x2 = 2 + -2 Combine like terms: -10 + -2 = -12 -12 + 0.9x + 0.03x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -12 + 0.9x + 0.03x2 = 0 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. -400 + 30x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + 30x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 30x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 30x + x2 = 0 + 400 30x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 30x + x2 = 400 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 400 + 225 Reorder the terms: 225 + 30x + x2 = 400 + 225 Combine like terms: 400 + 225 = 625 225 + 30x + x2 = 625 Factor a perfect square on the left side: (x + 15)(x + 15) = 625 Calculate the square root of the right side: 25 Break this problem into two subproblems by setting (x + 15) equal to 25 and -25.Subproblem 1
x + 15 = 25 Simplifying x + 15 = 25 Reorder the terms: 15 + x = 25 Solving 15 + x = 25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 25 + -15 Combine like terms: 15 + -15 = 0 0 + x = 25 + -15 x = 25 + -15 Combine like terms: 25 + -15 = 10 x = 10 Simplifying x = 10Subproblem 2
x + 15 = -25 Simplifying x + 15 = -25 Reorder the terms: 15 + x = -25 Solving 15 + x = -25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -25 + -15 Combine like terms: 15 + -15 = 0 0 + x = -25 + -15 x = -25 + -15 Combine like terms: -25 + -15 = -40 x = -40 Simplifying x = -40Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -40}
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