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Simplifying 0.6(x + 80) * 1.2x = 129 Reorder the terms: 0.6(80 + x) * 1.2x = 129 Reorder the terms for easier multiplication: 0.6 * 1.2x(80 + x) = 129 Multiply 0.6 * 1.2 0.72x(80 + x) = 129 (80 * 0.72x + x * 0.72x) = 129 (57.6x + 0.72x2) = 129 Solving 57.6x + 0.72x2 = 129 Solving for variable 'x'. Reorder the terms: -129 + 57.6x + 0.72x2 = 129 + -129 Combine like terms: 129 + -129 = 0 -129 + 57.6x + 0.72x2 = 0 Begin completing the square. Divide all terms by 0.72 the coefficient of the squared term: Divide each side by '0.72'. -179.1666667 + 80x + x2 = 0 Move the constant term to the right: Add '179.1666667' to each side of the equation. -179.1666667 + 80x + 179.1666667 + x2 = 0 + 179.1666667 Reorder the terms: -179.1666667 + 179.1666667 + 80x + x2 = 0 + 179.1666667 Combine like terms: -179.1666667 + 179.1666667 = 0.0000000 0.0000000 + 80x + x2 = 0 + 179.1666667 80x + x2 = 0 + 179.1666667 Combine like terms: 0 + 179.1666667 = 179.1666667 80x + x2 = 179.1666667 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = 179.1666667 + 1600 Reorder the terms: 1600 + 80x + x2 = 179.1666667 + 1600 Combine like terms: 179.1666667 + 1600 = 1779.1666667 1600 + 80x + x2 = 1779.1666667 Factor a perfect square on the left side: (x + 40)(x + 40) = 1779.1666667 Calculate the square root of the right side: 42.180169117 Break this problem into two subproblems by setting (x + 40) equal to 42.180169117 and -42.180169117.Subproblem 1
x + 40 = 42.180169117 Simplifying x + 40 = 42.180169117 Reorder the terms: 40 + x = 42.180169117 Solving 40 + x = 42.180169117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 42.180169117 + -40 Combine like terms: 40 + -40 = 0 0 + x = 42.180169117 + -40 x = 42.180169117 + -40 Combine like terms: 42.180169117 + -40 = 2.180169117 x = 2.180169117 Simplifying x = 2.180169117Subproblem 2
x + 40 = -42.180169117 Simplifying x + 40 = -42.180169117 Reorder the terms: 40 + x = -42.180169117 Solving 40 + x = -42.180169117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -42.180169117 + -40 Combine like terms: 40 + -40 = 0 0 + x = -42.180169117 + -40 x = -42.180169117 + -40 Combine like terms: -42.180169117 + -40 = -82.180169117 x = -82.180169117 Simplifying x = -82.180169117Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.180169117, -82.180169117}
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