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Simplifying x2 + -21x + -49 = 0 Reorder the terms: -49 + -21x + x2 = 0 Solving -49 + -21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -21x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -21x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -21x + x2 = 0 + 49 -21x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -21x + x2 = 49 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 49 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 49 + 110.25 Combine like terms: 49 + 110.25 = 159.25 110.25 + -21x + x2 = 159.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 159.25 Calculate the square root of the right side: 12.619429464 Break this problem into two subproblems by setting (x + -10.5) equal to 12.619429464 and -12.619429464.Subproblem 1
x + -10.5 = 12.619429464 Simplifying x + -10.5 = 12.619429464 Reorder the terms: -10.5 + x = 12.619429464 Solving -10.5 + x = 12.619429464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 12.619429464 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 12.619429464 + 10.5 x = 12.619429464 + 10.5 Combine like terms: 12.619429464 + 10.5 = 23.119429464 x = 23.119429464 Simplifying x = 23.119429464Subproblem 2
x + -10.5 = -12.619429464 Simplifying x + -10.5 = -12.619429464 Reorder the terms: -10.5 + x = -12.619429464 Solving -10.5 + x = -12.619429464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -12.619429464 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -12.619429464 + 10.5 x = -12.619429464 + 10.5 Combine like terms: -12.619429464 + 10.5 = -2.119429464 x = -2.119429464 Simplifying x = -2.119429464Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.119429464, -2.119429464}
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