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Simplifying x2 + -12.56x + 6.67 = 0 Reorder the terms: 6.67 + -12.56x + x2 = 0 Solving 6.67 + -12.56x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6.67' to each side of the equation. 6.67 + -12.56x + -6.67 + x2 = 0 + -6.67 Reorder the terms: 6.67 + -6.67 + -12.56x + x2 = 0 + -6.67 Combine like terms: 6.67 + -6.67 = 0.00 0.00 + -12.56x + x2 = 0 + -6.67 -12.56x + x2 = 0 + -6.67 Combine like terms: 0 + -6.67 = -6.67 -12.56x + x2 = -6.67 The x term is -12.56x. Take half its coefficient (-6.28). Square it (39.4384) and add it to both sides. Add '39.4384' to each side of the equation. -12.56x + 39.4384 + x2 = -6.67 + 39.4384 Reorder the terms: 39.4384 + -12.56x + x2 = -6.67 + 39.4384 Combine like terms: -6.67 + 39.4384 = 32.7684 39.4384 + -12.56x + x2 = 32.7684 Factor a perfect square on the left side: (x + -6.28)(x + -6.28) = 32.7684 Calculate the square root of the right side: 5.724368961 Break this problem into two subproblems by setting (x + -6.28) equal to 5.724368961 and -5.724368961.Subproblem 1
x + -6.28 = 5.724368961 Simplifying x + -6.28 = 5.724368961 Reorder the terms: -6.28 + x = 5.724368961 Solving -6.28 + x = 5.724368961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.28' to each side of the equation. -6.28 + 6.28 + x = 5.724368961 + 6.28 Combine like terms: -6.28 + 6.28 = 0.00 0.00 + x = 5.724368961 + 6.28 x = 5.724368961 + 6.28 Combine like terms: 5.724368961 + 6.28 = 12.004368961 x = 12.004368961 Simplifying x = 12.004368961Subproblem 2
x + -6.28 = -5.724368961 Simplifying x + -6.28 = -5.724368961 Reorder the terms: -6.28 + x = -5.724368961 Solving -6.28 + x = -5.724368961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.28' to each side of the equation. -6.28 + 6.28 + x = -5.724368961 + 6.28 Combine like terms: -6.28 + 6.28 = 0.00 0.00 + x = -5.724368961 + 6.28 x = -5.724368961 + 6.28 Combine like terms: -5.724368961 + 6.28 = 0.555631039 x = 0.555631039 Simplifying x = 0.555631039Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.004368961, 0.555631039}
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