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Simplifying -0.9x2 + 73x = 0.6x2 + 10x + 588 Reorder the terms: 73x + -0.9x2 = 0.6x2 + 10x + 588 Reorder the terms: 73x + -0.9x2 = 588 + 10x + 0.6x2 Solving 73x + -0.9x2 = 588 + 10x + 0.6x2 Solving for variable 'x'. Reorder the terms: -588 + 73x + -10x + -0.9x2 + -0.6x2 = 588 + 10x + 0.6x2 + -588 + -10x + -0.6x2 Combine like terms: 73x + -10x = 63x -588 + 63x + -0.9x2 + -0.6x2 = 588 + 10x + 0.6x2 + -588 + -10x + -0.6x2 Combine like terms: -0.9x2 + -0.6x2 = -1.5x2 -588 + 63x + -1.5x2 = 588 + 10x + 0.6x2 + -588 + -10x + -0.6x2 Reorder the terms: -588 + 63x + -1.5x2 = 588 + -588 + 10x + -10x + 0.6x2 + -0.6x2 Combine like terms: 588 + -588 = 0 -588 + 63x + -1.5x2 = 0 + 10x + -10x + 0.6x2 + -0.6x2 -588 + 63x + -1.5x2 = 10x + -10x + 0.6x2 + -0.6x2 Combine like terms: 10x + -10x = 0 -588 + 63x + -1.5x2 = 0 + 0.6x2 + -0.6x2 -588 + 63x + -1.5x2 = 0.6x2 + -0.6x2 Combine like terms: 0.6x2 + -0.6x2 = 0.0 -588 + 63x + -1.5x2 = 0.0 Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. 392 + -42x + x2 = 0 Move the constant term to the right: Add '-392' to each side of the equation. 392 + -42x + -392 + x2 = 0 + -392 Reorder the terms: 392 + -392 + -42x + x2 = 0 + -392 Combine like terms: 392 + -392 = 0 0 + -42x + x2 = 0 + -392 -42x + x2 = 0 + -392 Combine like terms: 0 + -392 = -392 -42x + x2 = -392 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = -392 + 441 Reorder the terms: 441 + -42x + x2 = -392 + 441 Combine like terms: -392 + 441 = 49 441 + -42x + x2 = 49 Factor a perfect square on the left side: (x + -21)(x + -21) = 49 Calculate the square root of the right side: 7 Break this problem into two subproblems by setting (x + -21) equal to 7 and -7.Subproblem 1
x + -21 = 7 Simplifying x + -21 = 7 Reorder the terms: -21 + x = 7 Solving -21 + x = 7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 7 + 21 Combine like terms: -21 + 21 = 0 0 + x = 7 + 21 x = 7 + 21 Combine like terms: 7 + 21 = 28 x = 28 Simplifying x = 28Subproblem 2
x + -21 = -7 Simplifying x + -21 = -7 Reorder the terms: -21 + x = -7 Solving -21 + x = -7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -7 + 21 Combine like terms: -21 + 21 = 0 0 + x = -7 + 21 x = -7 + 21 Combine like terms: -7 + 21 = 14 x = 14 Simplifying x = 14Solution
The solution to the problem is based on the solutions from the subproblems. x = {28, 14}
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