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Simplifying x = 4x + 0.1x2 + -296.4 Reorder the terms: x = -296.4 + 4x + 0.1x2 Solving x = -296.4 + 4x + 0.1x2 Solving for variable 'x'. Reorder the terms: 296.4 + x + -4x + -0.1x2 = -296.4 + 4x + 0.1x2 + 296.4 + -4x + -0.1x2 Combine like terms: x + -4x = -3x 296.4 + -3x + -0.1x2 = -296.4 + 4x + 0.1x2 + 296.4 + -4x + -0.1x2 Reorder the terms: 296.4 + -3x + -0.1x2 = -296.4 + 296.4 + 4x + -4x + 0.1x2 + -0.1x2 Combine like terms: -296.4 + 296.4 = 0.0 296.4 + -3x + -0.1x2 = 0.0 + 4x + -4x + 0.1x2 + -0.1x2 296.4 + -3x + -0.1x2 = 4x + -4x + 0.1x2 + -0.1x2 Combine like terms: 4x + -4x = 0 296.4 + -3x + -0.1x2 = 0 + 0.1x2 + -0.1x2 296.4 + -3x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 296.4 + -3x + -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'. -2964 + 30x + x2 = 0 Move the constant term to the right: Add '2964' to each side of the equation. -2964 + 30x + 2964 + x2 = 0 + 2964 Reorder the terms: -2964 + 2964 + 30x + x2 = 0 + 2964 Combine like terms: -2964 + 2964 = 0 0 + 30x + x2 = 0 + 2964 30x + x2 = 0 + 2964 Combine like terms: 0 + 2964 = 2964 30x + x2 = 2964 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 2964 + 225 Reorder the terms: 225 + 30x + x2 = 2964 + 225 Combine like terms: 2964 + 225 = 3189 225 + 30x + x2 = 3189 Factor a perfect square on the left side: (x + 15)(x + 15) = 3189 Calculate the square root of the right side: 56.471231614 Break this problem into two subproblems by setting (x + 15) equal to 56.471231614 and -56.471231614.Subproblem 1
x + 15 = 56.471231614 Simplifying x + 15 = 56.471231614 Reorder the terms: 15 + x = 56.471231614 Solving 15 + x = 56.471231614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 56.471231614 + -15 Combine like terms: 15 + -15 = 0 0 + x = 56.471231614 + -15 x = 56.471231614 + -15 Combine like terms: 56.471231614 + -15 = 41.471231614 x = 41.471231614 Simplifying x = 41.471231614Subproblem 2
x + 15 = -56.471231614 Simplifying x + 15 = -56.471231614 Reorder the terms: 15 + x = -56.471231614 Solving 15 + x = -56.471231614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -56.471231614 + -15 Combine like terms: 15 + -15 = 0 0 + x = -56.471231614 + -15 x = -56.471231614 + -15 Combine like terms: -56.471231614 + -15 = -71.471231614 x = -71.471231614 Simplifying x = -71.471231614Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.471231614, -71.471231614}
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