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Simplifying 0.45(18) + 0.05 = 0.15x(12 + x) Multiply 0.45 * 18 8.1 + 0.05 = 0.15x(12 + x) Combine like terms: 8.1 + 0.05 = 8.15 8.15 = 0.15x(12 + x) 8.15 = (12 * 0.15x + x * 0.15x) 8.15 = (1.8x + 0.15x2) Solving 8.15 = 1.8x + 0.15x2 Solving for variable 'x'. Reorder the terms: 8.15 + -1.8x + -0.15x2 = 1.8x + -1.8x + 0.15x2 + -0.15x2 Combine like terms: 1.8x + -1.8x = 0.0 8.15 + -1.8x + -0.15x2 = 0.0 + 0.15x2 + -0.15x2 8.15 + -1.8x + -0.15x2 = 0.15x2 + -0.15x2 Combine like terms: 0.15x2 + -0.15x2 = 0.00 8.15 + -1.8x + -0.15x2 = 0.00 Begin completing the square. Divide all terms by -0.15 the coefficient of the squared term: Divide each side by '-0.15'. -54.33333333 + 12x + x2 = 0 Move the constant term to the right: Add '54.33333333' to each side of the equation. -54.33333333 + 12x + 54.33333333 + x2 = 0 + 54.33333333 Reorder the terms: -54.33333333 + 54.33333333 + 12x + x2 = 0 + 54.33333333 Combine like terms: -54.33333333 + 54.33333333 = 0.00000000 0.00000000 + 12x + x2 = 0 + 54.33333333 12x + x2 = 0 + 54.33333333 Combine like terms: 0 + 54.33333333 = 54.33333333 12x + x2 = 54.33333333 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 54.33333333 + 36 Reorder the terms: 36 + 12x + x2 = 54.33333333 + 36 Combine like terms: 54.33333333 + 36 = 90.33333333 36 + 12x + x2 = 90.33333333 Factor a perfect square on the left side: (x + 6)(x + 6) = 90.33333333 Calculate the square root of the right side: 9.504384953 Break this problem into two subproblems by setting (x + 6) equal to 9.504384953 and -9.504384953.Subproblem 1
x + 6 = 9.504384953 Simplifying x + 6 = 9.504384953 Reorder the terms: 6 + x = 9.504384953 Solving 6 + x = 9.504384953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 9.504384953 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.504384953 + -6 x = 9.504384953 + -6 Combine like terms: 9.504384953 + -6 = 3.504384953 x = 3.504384953 Simplifying x = 3.504384953Subproblem 2
x + 6 = -9.504384953 Simplifying x + 6 = -9.504384953 Reorder the terms: 6 + x = -9.504384953 Solving 6 + x = -9.504384953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -9.504384953 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.504384953 + -6 x = -9.504384953 + -6 Combine like terms: -9.504384953 + -6 = -15.504384953 x = -15.504384953 Simplifying x = -15.504384953Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.504384953, -15.504384953}
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