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Simplifying 4x(x + -5) + -5 = 6x + 7.4 + -4x Reorder the terms: 4x(-5 + x) + -5 = 6x + 7.4 + -4x (-5 * 4x + x * 4x) + -5 = 6x + 7.4 + -4x (-20x + 4x2) + -5 = 6x + 7.4 + -4x Reorder the terms: -5 + -20x + 4x2 = 6x + 7.4 + -4x Reorder the terms: -5 + -20x + 4x2 = 7.4 + 6x + -4x Combine like terms: 6x + -4x = 2x -5 + -20x + 4x2 = 7.4 + 2x Solving -5 + -20x + 4x2 = 7.4 + 2x Solving for variable 'x'. Reorder the terms: -5 + -7.4 + -20x + -2x + 4x2 = 7.4 + 2x + -7.4 + -2x Combine like terms: -5 + -7.4 = -12.4 -12.4 + -20x + -2x + 4x2 = 7.4 + 2x + -7.4 + -2x Combine like terms: -20x + -2x = -22x -12.4 + -22x + 4x2 = 7.4 + 2x + -7.4 + -2x Reorder the terms: -12.4 + -22x + 4x2 = 7.4 + -7.4 + 2x + -2x Combine like terms: 7.4 + -7.4 = 0.0 -12.4 + -22x + 4x2 = 0.0 + 2x + -2x -12.4 + -22x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -12.4 + -22x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.1 + -5.5x + x2 = 0 Move the constant term to the right: Add '3.1' to each side of the equation. -3.1 + -5.5x + 3.1 + x2 = 0 + 3.1 Reorder the terms: -3.1 + 3.1 + -5.5x + x2 = 0 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + -5.5x + x2 = 0 + 3.1 -5.5x + x2 = 0 + 3.1 Combine like terms: 0 + 3.1 = 3.1 -5.5x + x2 = 3.1 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 3.1 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 3.1 + 7.5625 Combine like terms: 3.1 + 7.5625 = 10.6625 7.5625 + -5.5x + x2 = 10.6625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 10.6625 Calculate the square root of the right side: 3.265348373 Break this problem into two subproblems by setting (x + -2.75) equal to 3.265348373 and -3.265348373.Subproblem 1
x + -2.75 = 3.265348373 Simplifying x + -2.75 = 3.265348373 Reorder the terms: -2.75 + x = 3.265348373 Solving -2.75 + x = 3.265348373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.265348373 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.265348373 + 2.75 x = 3.265348373 + 2.75 Combine like terms: 3.265348373 + 2.75 = 6.015348373 x = 6.015348373 Simplifying x = 6.015348373Subproblem 2
x + -2.75 = -3.265348373 Simplifying x + -2.75 = -3.265348373 Reorder the terms: -2.75 + x = -3.265348373 Solving -2.75 + x = -3.265348373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.265348373 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.265348373 + 2.75 x = -3.265348373 + 2.75 Combine like terms: -3.265348373 + 2.75 = -0.515348373 x = -0.515348373 Simplifying x = -0.515348373Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.015348373, -0.515348373}
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