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Simplifying 10 + 4x = 5x(x + -6) + 33 Reorder the terms: 10 + 4x = 5x(-6 + x) + 33 10 + 4x = (-6 * 5x + x * 5x) + 33 10 + 4x = (-30x + 5x2) + 33 Reorder the terms: 10 + 4x = 33 + -30x + 5x2 Solving 10 + 4x = 33 + -30x + 5x2 Solving for variable 'x'. Reorder the terms: 10 + -33 + 4x + 30x + -5x2 = 33 + -30x + 5x2 + -33 + 30x + -5x2 Combine like terms: 10 + -33 = -23 -23 + 4x + 30x + -5x2 = 33 + -30x + 5x2 + -33 + 30x + -5x2 Combine like terms: 4x + 30x = 34x -23 + 34x + -5x2 = 33 + -30x + 5x2 + -33 + 30x + -5x2 Reorder the terms: -23 + 34x + -5x2 = 33 + -33 + -30x + 30x + 5x2 + -5x2 Combine like terms: 33 + -33 = 0 -23 + 34x + -5x2 = 0 + -30x + 30x + 5x2 + -5x2 -23 + 34x + -5x2 = -30x + 30x + 5x2 + -5x2 Combine like terms: -30x + 30x = 0 -23 + 34x + -5x2 = 0 + 5x2 + -5x2 -23 + 34x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -23 + 34x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 4.6 + -6.8x + x2 = 0 Move the constant term to the right: Add '-4.6' to each side of the equation. 4.6 + -6.8x + -4.6 + x2 = 0 + -4.6 Reorder the terms: 4.6 + -4.6 + -6.8x + x2 = 0 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + -6.8x + x2 = 0 + -4.6 -6.8x + x2 = 0 + -4.6 Combine like terms: 0 + -4.6 = -4.6 -6.8x + x2 = -4.6 The x term is -6.8x. Take half its coefficient (-3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. -6.8x + 11.56 + x2 = -4.6 + 11.56 Reorder the terms: 11.56 + -6.8x + x2 = -4.6 + 11.56 Combine like terms: -4.6 + 11.56 = 6.96 11.56 + -6.8x + x2 = 6.96 Factor a perfect square on the left side: (x + -3.4)(x + -3.4) = 6.96 Calculate the square root of the right side: 2.638181192 Break this problem into two subproblems by setting (x + -3.4) equal to 2.638181192 and -2.638181192.Subproblem 1
x + -3.4 = 2.638181192 Simplifying x + -3.4 = 2.638181192 Reorder the terms: -3.4 + x = 2.638181192 Solving -3.4 + x = 2.638181192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = 2.638181192 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = 2.638181192 + 3.4 x = 2.638181192 + 3.4 Combine like terms: 2.638181192 + 3.4 = 6.038181192 x = 6.038181192 Simplifying x = 6.038181192Subproblem 2
x + -3.4 = -2.638181192 Simplifying x + -3.4 = -2.638181192 Reorder the terms: -3.4 + x = -2.638181192 Solving -3.4 + x = -2.638181192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = -2.638181192 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = -2.638181192 + 3.4 x = -2.638181192 + 3.4 Combine like terms: -2.638181192 + 3.4 = 0.761818808 x = 0.761818808 Simplifying x = 0.761818808Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.038181192, 0.761818808}
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