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Simplifying x2 + -29x + 40 = 0 Reorder the terms: 40 + -29x + x2 = 0 Solving 40 + -29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -29x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -29x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -29x + x2 = 0 + -40 -29x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -29x + x2 = -40 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 = -40 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -40 + 210.25 Combine like terms: -40 + 210.25 = 170.25 210.25 + -29x + x2 = 170.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 170.25 Calculate the square root of the right side: 13.047988351 Break this problem into two subproblems by setting (x + -14.5) equal to 13.047988351 and -13.047988351.Subproblem 1
x + -14.5 = 13.047988351 Simplifying x + -14.5 = 13.047988351 Reorder the terms: -14.5 + x = 13.047988351 Solving -14.5 + x = 13.047988351 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 = 13.047988351 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 13.047988351 + 14.5 x = 13.047988351 + 14.5 Combine like terms: 13.047988351 + 14.5 = 27.547988351 x = 27.547988351 Simplifying x = 27.547988351Subproblem 2
x + -14.5 = -13.047988351 Simplifying x + -14.5 = -13.047988351 Reorder the terms: -14.5 + x = -13.047988351 Solving -14.5 + x = -13.047988351 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 = -13.047988351 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -13.047988351 + 14.5 x = -13.047988351 + 14.5 Combine like terms: -13.047988351 + 14.5 = 1.452011649 x = 1.452011649 Simplifying x = 1.452011649Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.547988351, 1.452011649}
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