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Simplifying x2 + -13x + 42.25 = 22.09 Reorder the terms: 42.25 + -13x + x2 = 22.09 Solving 42.25 + -13x + x2 = 22.09 Solving for variable 'x'. Reorder the terms: 42.25 + -22.09 + -13x + x2 = 22.09 + -22.09 Combine like terms: 42.25 + -22.09 = 20.16 20.16 + -13x + x2 = 22.09 + -22.09 Combine like terms: 22.09 + -22.09 = 0.00 20.16 + -13x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-20.16' to each side of the equation. 20.16 + -13x + -20.16 + x2 = 0.00 + -20.16 Reorder the terms: 20.16 + -20.16 + -13x + x2 = 0.00 + -20.16 Combine like terms: 20.16 + -20.16 = 0.00 0.00 + -13x + x2 = 0.00 + -20.16 -13x + x2 = 0.00 + -20.16 Combine like terms: 0.00 + -20.16 = -20.16 -13x + x2 = -20.16 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -20.16 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -20.16 + 42.25 Combine like terms: -20.16 + 42.25 = 22.09 42.25 + -13x + x2 = 22.09 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 22.09 Calculate the square root of the right side: 4.7 Break this problem into two subproblems by setting (x + -6.5) equal to 4.7 and -4.7.Subproblem 1
x + -6.5 = 4.7 Simplifying x + -6.5 = 4.7 Reorder the terms: -6.5 + x = 4.7 Solving -6.5 + x = 4.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 4.7 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 4.7 + 6.5 x = 4.7 + 6.5 Combine like terms: 4.7 + 6.5 = 11.2 x = 11.2 Simplifying x = 11.2Subproblem 2
x + -6.5 = -4.7 Simplifying x + -6.5 = -4.7 Reorder the terms: -6.5 + x = -4.7 Solving -6.5 + x = -4.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -4.7 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -4.7 + 6.5 x = -4.7 + 6.5 Combine like terms: -4.7 + 6.5 = 1.8 x = 1.8 Simplifying x = 1.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.2, 1.8}
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