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Simplifying 0.80x + 0.05x(18 + -1x) = 0.10(-36) 0.80x + (18 * 0.05x + -1x * 0.05x) = 0.10(-36) 0.80x + (0.9x + -0.05x2) = 0.10(-36) Combine like terms: 0.80x + 0.9x = 1.7x 1.7x + -0.05x2 = 0.10(-36) Multiply 0.10 * -36 1.7x + -0.05x2 = -3.6 Solving 1.7x + -0.05x2 = -3.6 Solving for variable 'x'. Reorder the terms: 3.6 + 1.7x + -0.05x2 = -3.6 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 3.6 + 1.7x + -0.05x2 = 0.0 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -72 + -34x + x2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + -34x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -34x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -34x + x2 = 0 + 72 -34x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -34x + x2 = 72 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = 72 + 289 Reorder the terms: 289 + -34x + x2 = 72 + 289 Combine like terms: 72 + 289 = 361 289 + -34x + x2 = 361 Factor a perfect square on the left side: (x + -17)(x + -17) = 361 Calculate the square root of the right side: 19 Break this problem into two subproblems by setting (x + -17) equal to 19 and -19.Subproblem 1
x + -17 = 19 Simplifying x + -17 = 19 Reorder the terms: -17 + x = 19 Solving -17 + x = 19 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 19 + 17 Combine like terms: -17 + 17 = 0 0 + x = 19 + 17 x = 19 + 17 Combine like terms: 19 + 17 = 36 x = 36 Simplifying x = 36Subproblem 2
x + -17 = -19 Simplifying x + -17 = -19 Reorder the terms: -17 + x = -19 Solving -17 + x = -19 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -19 + 17 Combine like terms: -17 + 17 = 0 0 + x = -19 + 17 x = -19 + 17 Combine like terms: -19 + 17 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {36, -2}
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