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Simplifying 3(2x + -5) = 5(x + -4) * 1x + 5 Reorder the terms: 3(-5 + 2x) = 5(x + -4) * 1x + 5 (-5 * 3 + 2x * 3) = 5(x + -4) * 1x + 5 (-15 + 6x) = 5(x + -4) * 1x + 5 Reorder the terms: -15 + 6x = 5(-4 + x) * 1x + 5 Reorder the terms for easier multiplication: -15 + 6x = 5 * 1x(-4 + x) + 5 Multiply 5 * 1 -15 + 6x = 5x(-4 + x) + 5 -15 + 6x = (-4 * 5x + x * 5x) + 5 -15 + 6x = (-20x + 5x2) + 5 Reorder the terms: -15 + 6x = 5 + -20x + 5x2 Solving -15 + 6x = 5 + -20x + 5x2 Solving for variable 'x'. Reorder the terms: -15 + -5 + 6x + 20x + -5x2 = 5 + -20x + 5x2 + -5 + 20x + -5x2 Combine like terms: -15 + -5 = -20 -20 + 6x + 20x + -5x2 = 5 + -20x + 5x2 + -5 + 20x + -5x2 Combine like terms: 6x + 20x = 26x -20 + 26x + -5x2 = 5 + -20x + 5x2 + -5 + 20x + -5x2 Reorder the terms: -20 + 26x + -5x2 = 5 + -5 + -20x + 20x + 5x2 + -5x2 Combine like terms: 5 + -5 = 0 -20 + 26x + -5x2 = 0 + -20x + 20x + 5x2 + -5x2 -20 + 26x + -5x2 = -20x + 20x + 5x2 + -5x2 Combine like terms: -20x + 20x = 0 -20 + 26x + -5x2 = 0 + 5x2 + -5x2 -20 + 26x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -20 + 26x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 4 + -5.2x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -5.2x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -5.2x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5.2x + x2 = 0 + -4 -5.2x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -5.2x + x2 = -4 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = -4 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = -4 + 6.76 Combine like terms: -4 + 6.76 = 2.76 6.76 + -5.2x + x2 = 2.76 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 2.76 Calculate the square root of the right side: 1.661324773 Break this problem into two subproblems by setting (x + -2.6) equal to 1.661324773 and -1.661324773.Subproblem 1
x + -2.6 = 1.661324773 Simplifying x + -2.6 = 1.661324773 Reorder the terms: -2.6 + x = 1.661324773 Solving -2.6 + x = 1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 1.661324773 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 1.661324773 + 2.6 x = 1.661324773 + 2.6 Combine like terms: 1.661324773 + 2.6 = 4.261324773 x = 4.261324773 Simplifying x = 4.261324773Subproblem 2
x + -2.6 = -1.661324773 Simplifying x + -2.6 = -1.661324773 Reorder the terms: -2.6 + x = -1.661324773 Solving -2.6 + x = -1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -1.661324773 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -1.661324773 + 2.6 x = -1.661324773 + 2.6 Combine like terms: -1.661324773 + 2.6 = 0.938675227 x = 0.938675227 Simplifying x = 0.938675227Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.261324773, 0.938675227}
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