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Simplifying 0.02x + 0.01x + 0.05x(2x) = 10.40 Remove parenthesis around (2x) 0.02x + 0.01x + 0.05x * 2x = 10.40 Reorder the terms for easier multiplication: 0.02x + 0.01x + 0.05 * 2x * x = 10.40 Multiply 0.05 * 2 0.02x + 0.01x + 0.1x * x = 10.40 Multiply x * x 0.02x + 0.01x + 0.1x2 = 10.40 Combine like terms: 0.02x + 0.01x = 0.03x 0.03x + 0.1x2 = 10.40 Solving 0.03x + 0.1x2 = 10.40 Solving for variable 'x'. Reorder the terms: -10.40 + 0.03x + 0.1x2 = 10.40 + -10.40 Combine like terms: 10.40 + -10.40 = 0.00 -10.40 + 0.03x + 0.1x2 = 0.00 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -104 + 0.3x + x2 = 0.0 Move the constant term to the right: Add '104' to each side of the equation. -104 + 0.3x + 104 + x2 = 0.0 + 104 Reorder the terms: -104 + 104 + 0.3x + x2 = 0.0 + 104 Combine like terms: -104 + 104 = 0 0 + 0.3x + x2 = 0.0 + 104 0.3x + x2 = 0.0 + 104 Combine like terms: 0.0 + 104 = 104 0.3x + x2 = 104 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 104 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 104 + 0.0225 Combine like terms: 104 + 0.0225 = 104.0225 0.0225 + 0.3x + x2 = 104.0225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 104.0225 Calculate the square root of the right side: 10.199142121 Break this problem into two subproblems by setting (x + 0.15) equal to 10.199142121 and -10.199142121.Subproblem 1
x + 0.15 = 10.199142121 Simplifying x + 0.15 = 10.199142121 Reorder the terms: 0.15 + x = 10.199142121 Solving 0.15 + x = 10.199142121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 10.199142121 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 10.199142121 + -0.15 x = 10.199142121 + -0.15 Combine like terms: 10.199142121 + -0.15 = 10.049142121 x = 10.049142121 Simplifying x = 10.049142121Subproblem 2
x + 0.15 = -10.199142121 Simplifying x + 0.15 = -10.199142121 Reorder the terms: 0.15 + x = -10.199142121 Solving 0.15 + x = -10.199142121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -10.199142121 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -10.199142121 + -0.15 x = -10.199142121 + -0.15 Combine like terms: -10.199142121 + -0.15 = -10.349142121 x = -10.349142121 Simplifying x = -10.349142121Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.049142121, -10.349142121}
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