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Simplifying 10x2 + -49x + 54 = 0 Reorder the terms: 54 + -49x + 10x2 = 0 Solving 54 + -49x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 5.4 + -4.9x + x2 = 0 Move the constant term to the right: Add '-5.4' to each side of the equation. 5.4 + -4.9x + -5.4 + x2 = 0 + -5.4 Reorder the terms: 5.4 + -5.4 + -4.9x + x2 = 0 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + -4.9x + x2 = 0 + -5.4 -4.9x + x2 = 0 + -5.4 Combine like terms: 0 + -5.4 = -5.4 -4.9x + x2 = -5.4 The x term is -4.9x. Take half its coefficient (-2.45). Square it (6.0025) and add it to both sides. Add '6.0025' to each side of the equation. -4.9x + 6.0025 + x2 = -5.4 + 6.0025 Reorder the terms: 6.0025 + -4.9x + x2 = -5.4 + 6.0025 Combine like terms: -5.4 + 6.0025 = 0.6025 6.0025 + -4.9x + x2 = 0.6025 Factor a perfect square on the left side: (x + -2.45)(x + -2.45) = 0.6025 Calculate the square root of the right side: 0.776208735 Break this problem into two subproblems by setting (x + -2.45) equal to 0.776208735 and -0.776208735.Subproblem 1
x + -2.45 = 0.776208735 Simplifying x + -2.45 = 0.776208735 Reorder the terms: -2.45 + x = 0.776208735 Solving -2.45 + x = 0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.45' to each side of the equation. -2.45 + 2.45 + x = 0.776208735 + 2.45 Combine like terms: -2.45 + 2.45 = 0.00 0.00 + x = 0.776208735 + 2.45 x = 0.776208735 + 2.45 Combine like terms: 0.776208735 + 2.45 = 3.226208735 x = 3.226208735 Simplifying x = 3.226208735Subproblem 2
x + -2.45 = -0.776208735 Simplifying x + -2.45 = -0.776208735 Reorder the terms: -2.45 + x = -0.776208735 Solving -2.45 + x = -0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.45' to each side of the equation. -2.45 + 2.45 + x = -0.776208735 + 2.45 Combine like terms: -2.45 + 2.45 = 0.00 0.00 + x = -0.776208735 + 2.45 x = -0.776208735 + 2.45 Combine like terms: -0.776208735 + 2.45 = 1.673791265 x = 1.673791265 Simplifying x = 1.673791265Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.226208735, 1.673791265}
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