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Simplifying x2 + -5.1x + 6.3 = 0 Reorder the terms: 6.3 + -5.1x + x2 = 0 Solving 6.3 + -5.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6.3' to each side of the equation. 6.3 + -5.1x + -6.3 + x2 = 0 + -6.3 Reorder the terms: 6.3 + -6.3 + -5.1x + x2 = 0 + -6.3 Combine like terms: 6.3 + -6.3 = 0.0 0.0 + -5.1x + x2 = 0 + -6.3 -5.1x + x2 = 0 + -6.3 Combine like terms: 0 + -6.3 = -6.3 -5.1x + x2 = -6.3 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 = -6.3 + 6.5025 Reorder the terms: 6.5025 + -5.1x + x2 = -6.3 + 6.5025 Combine like terms: -6.3 + 6.5025 = 0.2025 6.5025 + -5.1x + x2 = 0.2025 Factor a perfect square on the left side: (x + -2.55)(x + -2.55) = 0.2025 Calculate the square root of the right side: 0.45 Break this problem into two subproblems by setting (x + -2.55) equal to 0.45 and -0.45.Subproblem 1
x + -2.55 = 0.45 Simplifying x + -2.55 = 0.45 Reorder the terms: -2.55 + x = 0.45 Solving -2.55 + x = 0.45 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 = 0.45 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + x = 0.45 + 2.55 x = 0.45 + 2.55 Combine like terms: 0.45 + 2.55 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -2.55 = -0.45 Simplifying x + -2.55 = -0.45 Reorder the terms: -2.55 + x = -0.45 Solving -2.55 + x = -0.45 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 = -0.45 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + x = -0.45 + 2.55 x = -0.45 + 2.55 Combine like terms: -0.45 + 2.55 = 2.1 x = 2.1 Simplifying x = 2.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, 2.1}
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