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Simplifying 0.2x(2x + -15) + 0.6x = 4.25 Reorder the terms: 0.2x(-15 + 2x) + 0.6x = 4.25 (-15 * 0.2x + 2x * 0.2x) + 0.6x = 4.25 (-3x + 0.4x2) + 0.6x = 4.25 Reorder the terms: -3x + 0.6x + 0.4x2 = 4.25 Combine like terms: -3x + 0.6x = -2.4x -2.4x + 0.4x2 = 4.25 Solving -2.4x + 0.4x2 = 4.25 Solving for variable 'x'. Reorder the terms: -4.25 + -2.4x + 0.4x2 = 4.25 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 -4.25 + -2.4x + 0.4x2 = 0.00 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -10.625 + -6x + x2 = 0.0 Move the constant term to the right: Add '10.625' to each side of the equation. -10.625 + -6x + 10.625 + x2 = 0.0 + 10.625 Reorder the terms: -10.625 + 10.625 + -6x + x2 = 0.0 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + -6x + x2 = 0.0 + 10.625 -6x + x2 = 0.0 + 10.625 Combine like terms: 0.0 + 10.625 = 10.625 -6x + x2 = 10.625 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 = 10.625 + 9 Reorder the terms: 9 + -6x + x2 = 10.625 + 9 Combine like terms: 10.625 + 9 = 19.625 9 + -6x + x2 = 19.625 Factor a perfect square on the left side: (x + -3)(x + -3) = 19.625 Calculate the square root of the right side: 4.430011287 Break this problem into two subproblems by setting (x + -3) equal to 4.430011287 and -4.430011287.Subproblem 1
x + -3 = 4.430011287 Simplifying x + -3 = 4.430011287 Reorder the terms: -3 + x = 4.430011287 Solving -3 + x = 4.430011287 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 = 4.430011287 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.430011287 + 3 x = 4.430011287 + 3 Combine like terms: 4.430011287 + 3 = 7.430011287 x = 7.430011287 Simplifying x = 7.430011287Subproblem 2
x + -3 = -4.430011287 Simplifying x + -3 = -4.430011287 Reorder the terms: -3 + x = -4.430011287 Solving -3 + x = -4.430011287 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 = -4.430011287 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.430011287 + 3 x = -4.430011287 + 3 Combine like terms: -4.430011287 + 3 = -1.430011287 x = -1.430011287 Simplifying x = -1.430011287Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.430011287, -1.430011287}
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