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Simplifying x2 + -29x + 115 = 0 Reorder the terms: 115 + -29x + x2 = 0 Solving 115 + -29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-115' to each side of the equation. 115 + -29x + -115 + x2 = 0 + -115 Reorder the terms: 115 + -115 + -29x + x2 = 0 + -115 Combine like terms: 115 + -115 = 0 0 + -29x + x2 = 0 + -115 -29x + x2 = 0 + -115 Combine like terms: 0 + -115 = -115 -29x + x2 = -115 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 = -115 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -115 + 210.25 Combine like terms: -115 + 210.25 = 95.25 210.25 + -29x + x2 = 95.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 95.25 Calculate the square root of the right side: 9.759610648 Break this problem into two subproblems by setting (x + -14.5) equal to 9.759610648 and -9.759610648.Subproblem 1
x + -14.5 = 9.759610648 Simplifying x + -14.5 = 9.759610648 Reorder the terms: -14.5 + x = 9.759610648 Solving -14.5 + x = 9.759610648 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 = 9.759610648 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 9.759610648 + 14.5 x = 9.759610648 + 14.5 Combine like terms: 9.759610648 + 14.5 = 24.259610648 x = 24.259610648 Simplifying x = 24.259610648Subproblem 2
x + -14.5 = -9.759610648 Simplifying x + -14.5 = -9.759610648 Reorder the terms: -14.5 + x = -9.759610648 Solving -14.5 + x = -9.759610648 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 = -9.759610648 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -9.759610648 + 14.5 x = -9.759610648 + 14.5 Combine like terms: -9.759610648 + 14.5 = 4.740389352 x = 4.740389352 Simplifying x = 4.740389352Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.259610648, 4.740389352}
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