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Simplifying x2 + -29x + 45 = 0 Reorder the terms: 45 + -29x + x2 = 0 Solving 45 + -29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -29x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -29x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -29x + x2 = 0 + -45 -29x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -29x + x2 = -45 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -45 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -45 + 210.25 Combine like terms: -45 + 210.25 = 165.25 210.25 + -29x + x2 = 165.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 165.25 Calculate the square root of the right side: 12.854960132 Break this problem into two subproblems by setting (x + -14.5) equal to 12.854960132 and -12.854960132.Subproblem 1
x + -14.5 = 12.854960132 Simplifying x + -14.5 = 12.854960132 Reorder the terms: -14.5 + x = 12.854960132 Solving -14.5 + x = 12.854960132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 12.854960132 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 12.854960132 + 14.5 x = 12.854960132 + 14.5 Combine like terms: 12.854960132 + 14.5 = 27.354960132 x = 27.354960132 Simplifying x = 27.354960132Subproblem 2
x + -14.5 = -12.854960132 Simplifying x + -14.5 = -12.854960132 Reorder the terms: -14.5 + x = -12.854960132 Solving -14.5 + x = -12.854960132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -12.854960132 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -12.854960132 + 14.5 x = -12.854960132 + 14.5 Combine like terms: -12.854960132 + 14.5 = 1.645039868 x = 1.645039868 Simplifying x = 1.645039868Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.354960132, 1.645039868}
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