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Simplifying x2 + -21x = -32 Reorder the terms: -21x + x2 = -32 Solving -21x + x2 = -32 Solving for variable 'x'. Reorder the terms: 32 + -21x + x2 = -32 + 32 Combine like terms: -32 + 32 = 0 32 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -21x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + -21x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -21x + x2 = 0 + -32 -21x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 -21x + x2 = -32 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 = -32 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -32 + 110.25 Combine like terms: -32 + 110.25 = 78.25 110.25 + -21x + x2 = 78.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + -10.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + -10.5 = 8.845903006 Simplifying x + -10.5 = 8.845903006 Reorder the terms: -10.5 + x = 8.845903006 Solving -10.5 + x = 8.845903006 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 = 8.845903006 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 8.845903006 + 10.5 x = 8.845903006 + 10.5 Combine like terms: 8.845903006 + 10.5 = 19.345903006 x = 19.345903006 Simplifying x = 19.345903006Subproblem 2
x + -10.5 = -8.845903006 Simplifying x + -10.5 = -8.845903006 Reorder the terms: -10.5 + x = -8.845903006 Solving -10.5 + x = -8.845903006 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 = -8.845903006 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -8.845903006 + 10.5 x = -8.845903006 + 10.5 Combine like terms: -8.845903006 + 10.5 = 1.654096994 x = 1.654096994 Simplifying x = 1.654096994Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.345903006, 1.654096994}
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