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Simplifying (0.3 + 2x)(0.8 + 2x) = 8.53618 Multiply (0.3 + 2x) * (0.8 + 2x) (0.3(0.8 + 2x) + 2x * (0.8 + 2x)) = 8.53618 ((0.8 * 0.3 + 2x * 0.3) + 2x * (0.8 + 2x)) = 8.53618 ((0.24 + 0.6x) + 2x * (0.8 + 2x)) = 8.53618 (0.24 + 0.6x + (0.8 * 2x + 2x * 2x)) = 8.53618 (0.24 + 0.6x + (1.6x + 4x2)) = 8.53618 Combine like terms: 0.6x + 1.6x = 2.2x (0.24 + 2.2x + 4x2) = 8.53618 Solving 0.24 + 2.2x + 4x2 = 8.53618 Solving for variable 'x'. Reorder the terms: 0.24 + -8.53618 + 2.2x + 4x2 = 8.53618 + -8.53618 Combine like terms: 0.24 + -8.53618 = -8.29618 -8.29618 + 2.2x + 4x2 = 8.53618 + -8.53618 Combine like terms: 8.53618 + -8.53618 = 0.00000 -8.29618 + 2.2x + 4x2 = 0.00000 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.074045 + 0.55x + x2 = 0.00000 Move the constant term to the right: Add '2.074045' to each side of the equation. -2.074045 + 0.55x + 2.074045 + x2 = 0.00000 + 2.074045 Reorder the terms: -2.074045 + 2.074045 + 0.55x + x2 = 0.00000 + 2.074045 Combine like terms: -2.074045 + 2.074045 = 0.000000 0.000000 + 0.55x + x2 = 0.00000 + 2.074045 0.55x + x2 = 0.00000 + 2.074045 Combine like terms: 0.00000 + 2.074045 = 2.074045 0.55x + x2 = 2.074045 The x term is 0.55x. Take half its coefficient (0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. 0.55x + 0.075625 + x2 = 2.074045 + 0.075625 Reorder the terms: 0.075625 + 0.55x + x2 = 2.074045 + 0.075625 Combine like terms: 2.074045 + 0.075625 = 2.14967 0.075625 + 0.55x + x2 = 2.14967 Factor a perfect square on the left side: (x + 0.275)(x + 0.275) = 2.14967 Calculate the square root of the right side: 1.466175296 Break this problem into two subproblems by setting (x + 0.275) equal to 1.466175296 and -1.466175296.Subproblem 1
x + 0.275 = 1.466175296 Simplifying x + 0.275 = 1.466175296 Reorder the terms: 0.275 + x = 1.466175296 Solving 0.275 + x = 1.466175296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.275' to each side of the equation. 0.275 + -0.275 + x = 1.466175296 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + x = 1.466175296 + -0.275 x = 1.466175296 + -0.275 Combine like terms: 1.466175296 + -0.275 = 1.191175296 x = 1.191175296 Simplifying x = 1.191175296Subproblem 2
x + 0.275 = -1.466175296 Simplifying x + 0.275 = -1.466175296 Reorder the terms: 0.275 + x = -1.466175296 Solving 0.275 + x = -1.466175296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.275' to each side of the equation. 0.275 + -0.275 + x = -1.466175296 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + x = -1.466175296 + -0.275 x = -1.466175296 + -0.275 Combine like terms: -1.466175296 + -0.275 = -1.741175296 x = -1.741175296 Simplifying x = -1.741175296Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.191175296, -1.741175296}
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