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Simplifying 0.4x2 + 3x + -135 = 0 Reorder the terms: -135 + 3x + 0.4x2 = 0 Solving -135 + 3x + 0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -337.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '337.5' to each side of the equation. -337.5 + 7.5x + 337.5 + x2 = 0 + 337.5 Reorder the terms: -337.5 + 337.5 + 7.5x + x2 = 0 + 337.5 Combine like terms: -337.5 + 337.5 = 0.0 0.0 + 7.5x + x2 = 0 + 337.5 7.5x + x2 = 0 + 337.5 Combine like terms: 0 + 337.5 = 337.5 7.5x + x2 = 337.5 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 337.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 337.5 + 14.0625 Combine like terms: 337.5 + 14.0625 = 351.5625 14.0625 + 7.5x + x2 = 351.5625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 351.5625 Calculate the square root of the right side: 18.75 Break this problem into two subproblems by setting (x + 3.75) equal to 18.75 and -18.75.Subproblem 1
x + 3.75 = 18.75 Simplifying x + 3.75 = 18.75 Reorder the terms: 3.75 + x = 18.75 Solving 3.75 + x = 18.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 18.75 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 18.75 + -3.75 x = 18.75 + -3.75 Combine like terms: 18.75 + -3.75 = 15 x = 15 Simplifying x = 15Subproblem 2
x + 3.75 = -18.75 Simplifying x + 3.75 = -18.75 Reorder the terms: 3.75 + x = -18.75 Solving 3.75 + x = -18.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -18.75 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -18.75 + -3.75 x = -18.75 + -3.75 Combine like terms: -18.75 + -3.75 = -22.5 x = -22.5 Simplifying x = -22.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {15, -22.5}
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