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Simplifying x2 + -13x + 4 = 17 Reorder the terms: 4 + -13x + x2 = 17 Solving 4 + -13x + x2 = 17 Solving for variable 'x'. Reorder the terms: 4 + -17 + -13x + x2 = 17 + -17 Combine like terms: 4 + -17 = -13 -13 + -13x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -13 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -13x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -13x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -13x + x2 = 0 + 13 -13x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -13x + x2 = 13 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 = 13 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 13 + 42.25 Combine like terms: 13 + 42.25 = 55.25 42.25 + -13x + x2 = 55.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + -6.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + -6.5 = 7.433034374 Simplifying x + -6.5 = 7.433034374 Reorder the terms: -6.5 + x = 7.433034374 Solving -6.5 + x = 7.433034374 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 = 7.433034374 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 7.433034374 + 6.5 x = 7.433034374 + 6.5 Combine like terms: 7.433034374 + 6.5 = 13.933034374 x = 13.933034374 Simplifying x = 13.933034374Subproblem 2
x + -6.5 = -7.433034374 Simplifying x + -6.5 = -7.433034374 Reorder the terms: -6.5 + x = -7.433034374 Solving -6.5 + x = -7.433034374 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 = -7.433034374 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -7.433034374 + 6.5 x = -7.433034374 + 6.5 Combine like terms: -7.433034374 + 6.5 = -0.933034374 x = -0.933034374 Simplifying x = -0.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.933034374, -0.933034374}
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