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Simplifying (x2) + -21x = -12 x2 + -21x = -12 Reorder the terms: -21x + x2 = -12 Solving -21x + x2 = -12 Solving for variable 'x'. Reorder the terms: 12 + -21x + x2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -21x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -21x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -21x + x2 = 0 + -12 -21x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -21x + x2 = -12 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 = -12 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -12 + 110.25 Combine like terms: -12 + 110.25 = 98.25 110.25 + -21x + x2 = 98.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 98.25 Calculate the square root of the right side: 9.912113801 Break this problem into two subproblems by setting (x + -10.5) equal to 9.912113801 and -9.912113801.Subproblem 1
x + -10.5 = 9.912113801 Simplifying x + -10.5 = 9.912113801 Reorder the terms: -10.5 + x = 9.912113801 Solving -10.5 + x = 9.912113801 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 = 9.912113801 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 9.912113801 + 10.5 x = 9.912113801 + 10.5 Combine like terms: 9.912113801 + 10.5 = 20.412113801 x = 20.412113801 Simplifying x = 20.412113801Subproblem 2
x + -10.5 = -9.912113801 Simplifying x + -10.5 = -9.912113801 Reorder the terms: -10.5 + x = -9.912113801 Solving -10.5 + x = -9.912113801 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 = -9.912113801 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -9.912113801 + 10.5 x = -9.912113801 + 10.5 Combine like terms: -9.912113801 + 10.5 = 0.587886199 x = 0.587886199 Simplifying x = 0.587886199Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.412113801, 0.587886199}
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