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Simplifying 0.35x + 0.09x(x + 4) = 0.03(12) Reorder the terms: 0.35x + 0.09x(4 + x) = 0.03(12) 0.35x + (4 * 0.09x + x * 0.09x) = 0.03(12) 0.35x + (0.36x + 0.09x2) = 0.03(12) Combine like terms: 0.35x + 0.36x = 0.71x 0.71x + 0.09x2 = 0.03(12) Multiply 0.03 * 12 0.71x + 0.09x2 = 0.36 Solving 0.71x + 0.09x2 = 0.36 Solving for variable 'x'. Reorder the terms: -0.36 + 0.71x + 0.09x2 = 0.36 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 -0.36 + 0.71x + 0.09x2 = 0.00 Begin completing the square. Divide all terms by 0.09 the coefficient of the squared term: Divide each side by '0.09'. -4 + 7.888888889x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 7.888888889x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 7.888888889x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7.888888889x + x2 = 0 + 4 7.888888889x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 7.888888889x + x2 = 4 The x term is 7.888888889x. Take half its coefficient (3.944444445). Square it (15.55864198) and add it to both sides. Add '15.55864198' to each side of the equation. 7.888888889x + 15.55864198 + x2 = 4 + 15.55864198 Reorder the terms: 15.55864198 + 7.888888889x + x2 = 4 + 15.55864198 Combine like terms: 4 + 15.55864198 = 19.55864198 15.55864198 + 7.888888889x + x2 = 19.55864198 Factor a perfect square on the left side: (x + 3.944444445)(x + 3.944444445) = 19.55864198 Calculate the square root of the right side: 4.422515345 Break this problem into two subproblems by setting (x + 3.944444445) equal to 4.422515345 and -4.422515345.Subproblem 1
x + 3.944444445 = 4.422515345 Simplifying x + 3.944444445 = 4.422515345 Reorder the terms: 3.944444445 + x = 4.422515345 Solving 3.944444445 + x = 4.422515345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.944444445' to each side of the equation. 3.944444445 + -3.944444445 + x = 4.422515345 + -3.944444445 Combine like terms: 3.944444445 + -3.944444445 = 0.000000000 0.000000000 + x = 4.422515345 + -3.944444445 x = 4.422515345 + -3.944444445 Combine like terms: 4.422515345 + -3.944444445 = 0.4780709 x = 0.4780709 Simplifying x = 0.4780709Subproblem 2
x + 3.944444445 = -4.422515345 Simplifying x + 3.944444445 = -4.422515345 Reorder the terms: 3.944444445 + x = -4.422515345 Solving 3.944444445 + x = -4.422515345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.944444445' to each side of the equation. 3.944444445 + -3.944444445 + x = -4.422515345 + -3.944444445 Combine like terms: 3.944444445 + -3.944444445 = 0.000000000 0.000000000 + x = -4.422515345 + -3.944444445 x = -4.422515345 + -3.944444445 Combine like terms: -4.422515345 + -3.944444445 = -8.36695979 x = -8.36695979 Simplifying x = -8.36695979Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4780709, -8.36695979}
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