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Simplifying 0.4x + -0.4x(0.4 + -0.1x) = 11.52 0.4x + (0.4 * -0.4x + -0.1x * -0.4x) = 11.52 0.4x + (-0.16x + 0.04x2) = 11.52 Combine like terms: 0.4x + -0.16x = 0.24x 0.24x + 0.04x2 = 11.52 Solving 0.24x + 0.04x2 = 11.52 Solving for variable 'x'. Reorder the terms: -11.52 + 0.24x + 0.04x2 = 11.52 + -11.52 Combine like terms: 11.52 + -11.52 = 0.00 -11.52 + 0.24x + 0.04x2 = 0.00 Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. -288 + 6x + x2 = 0 Move the constant term to the right: Add '288' to each side of the equation. -288 + 6x + 288 + x2 = 0 + 288 Reorder the terms: -288 + 288 + 6x + x2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 6x + x2 = 0 + 288 6x + x2 = 0 + 288 Combine like terms: 0 + 288 = 288 6x + x2 = 288 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 288 + 9 Reorder the terms: 9 + 6x + x2 = 288 + 9 Combine like terms: 288 + 9 = 297 9 + 6x + x2 = 297 Factor a perfect square on the left side: (x + 3)(x + 3) = 297 Calculate the square root of the right side: 17.23368794 Break this problem into two subproblems by setting (x + 3) equal to 17.23368794 and -17.23368794.Subproblem 1
x + 3 = 17.23368794 Simplifying x + 3 = 17.23368794 Reorder the terms: 3 + x = 17.23368794 Solving 3 + x = 17.23368794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 17.23368794 + -3 Combine like terms: 3 + -3 = 0 0 + x = 17.23368794 + -3 x = 17.23368794 + -3 Combine like terms: 17.23368794 + -3 = 14.23368794 x = 14.23368794 Simplifying x = 14.23368794Subproblem 2
x + 3 = -17.23368794 Simplifying x + 3 = -17.23368794 Reorder the terms: 3 + x = -17.23368794 Solving 3 + x = -17.23368794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -17.23368794 + -3 Combine like terms: 3 + -3 = 0 0 + x = -17.23368794 + -3 x = -17.23368794 + -3 Combine like terms: -17.23368794 + -3 = -20.23368794 x = -20.23368794 Simplifying x = -20.23368794Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.23368794, -20.23368794}
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