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Simplifying x2 + -5.1x + 4.9 = 0 Reorder the terms: 4.9 + -5.1x + x2 = 0 Solving 4.9 + -5.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4.9' to each side of the equation. 4.9 + -5.1x + -4.9 + x2 = 0 + -4.9 Reorder the terms: 4.9 + -4.9 + -5.1x + x2 = 0 + -4.9 Combine like terms: 4.9 + -4.9 = 0.0 0.0 + -5.1x + x2 = 0 + -4.9 -5.1x + x2 = 0 + -4.9 Combine like terms: 0 + -4.9 = -4.9 -5.1x + x2 = -4.9 The x term is -5.1x. Take half its coefficient (-2.55). Square it (6.5025) and add it to both sides. Add '6.5025' to each side of the equation. -5.1x + 6.5025 + x2 = -4.9 + 6.5025 Reorder the terms: 6.5025 + -5.1x + x2 = -4.9 + 6.5025 Combine like terms: -4.9 + 6.5025 = 1.6025 6.5025 + -5.1x + x2 = 1.6025 Factor a perfect square on the left side: (x + -2.55)(x + -2.55) = 1.6025 Calculate the square root of the right side: 1.26589889 Break this problem into two subproblems by setting (x + -2.55) equal to 1.26589889 and -1.26589889.Subproblem 1
x + -2.55 = 1.26589889 Simplifying x + -2.55 = 1.26589889 Reorder the terms: -2.55 + x = 1.26589889 Solving -2.55 + x = 1.26589889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.55' to each side of the equation. -2.55 + 2.55 + x = 1.26589889 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + x = 1.26589889 + 2.55 x = 1.26589889 + 2.55 Combine like terms: 1.26589889 + 2.55 = 3.81589889 x = 3.81589889 Simplifying x = 3.81589889Subproblem 2
x + -2.55 = -1.26589889 Simplifying x + -2.55 = -1.26589889 Reorder the terms: -2.55 + x = -1.26589889 Solving -2.55 + x = -1.26589889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.55' to each side of the equation. -2.55 + 2.55 + x = -1.26589889 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + x = -1.26589889 + 2.55 x = -1.26589889 + 2.55 Combine like terms: -1.26589889 + 2.55 = 1.28410111 x = 1.28410111 Simplifying x = 1.28410111Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.81589889, 1.28410111}
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