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Simplifying 0.4x + -3 = 0.1x(x + 30) Reorder the terms: -3 + 0.4x = 0.1x(x + 30) Reorder the terms: -3 + 0.4x = 0.1x(30 + x) -3 + 0.4x = (30 * 0.1x + x * 0.1x) -3 + 0.4x = (3x + 0.1x2) Solving -3 + 0.4x = 3x + 0.1x2 Solving for variable 'x'. Combine like terms: 0.4x + -3x = -2.6x -3 + -2.6x + -0.1x2 = 3x + 0.1x2 + -3x + -0.1x2 Reorder the terms: -3 + -2.6x + -0.1x2 = 3x + -3x + 0.1x2 + -0.1x2 Combine like terms: 3x + -3x = 0 -3 + -2.6x + -0.1x2 = 0 + 0.1x2 + -0.1x2 -3 + -2.6x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 -3 + -2.6x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 30 + 26x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + 26x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 26x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 26x + x2 = 0 + -30 26x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 26x + x2 = -30 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -30 + 169 Reorder the terms: 169 + 26x + x2 = -30 + 169 Combine like terms: -30 + 169 = 139 169 + 26x + x2 = 139 Factor a perfect square on the left side: (x + 13)(x + 13) = 139 Calculate the square root of the right side: 11.789826123 Break this problem into two subproblems by setting (x + 13) equal to 11.789826123 and -11.789826123.Subproblem 1
x + 13 = 11.789826123 Simplifying x + 13 = 11.789826123 Reorder the terms: 13 + x = 11.789826123 Solving 13 + x = 11.789826123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 11.789826123 + -13 Combine like terms: 13 + -13 = 0 0 + x = 11.789826123 + -13 x = 11.789826123 + -13 Combine like terms: 11.789826123 + -13 = -1.210173877 x = -1.210173877 Simplifying x = -1.210173877Subproblem 2
x + 13 = -11.789826123 Simplifying x + 13 = -11.789826123 Reorder the terms: 13 + x = -11.789826123 Solving 13 + x = -11.789826123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -11.789826123 + -13 Combine like terms: 13 + -13 = 0 0 + x = -11.789826123 + -13 x = -11.789826123 + -13 Combine like terms: -11.789826123 + -13 = -24.789826123 x = -24.789826123 Simplifying x = -24.789826123Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.210173877, -24.789826123}
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