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Simplifying x2 = 7x + 43 Reorder the terms: x2 = 43 + 7x Solving x2 = 43 + 7x Solving for variable 'x'. Reorder the terms: -43 + -7x + x2 = 43 + 7x + -43 + -7x Reorder the terms: -43 + -7x + x2 = 43 + -43 + 7x + -7x Combine like terms: 43 + -43 = 0 -43 + -7x + x2 = 0 + 7x + -7x -43 + -7x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -43 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -7x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + -7x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -7x + x2 = 0 + 43 -7x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 -7x + x2 = 43 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 43 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 43 + 12.25 Combine like terms: 43 + 12.25 = 55.25 12.25 + -7x + x2 = 55.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + -3.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + -3.5 = 7.433034374 Simplifying x + -3.5 = 7.433034374 Reorder the terms: -3.5 + x = 7.433034374 Solving -3.5 + x = 7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 7.433034374 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 7.433034374 + 3.5 x = 7.433034374 + 3.5 Combine like terms: 7.433034374 + 3.5 = 10.933034374 x = 10.933034374 Simplifying x = 10.933034374Subproblem 2
x + -3.5 = -7.433034374 Simplifying x + -3.5 = -7.433034374 Reorder the terms: -3.5 + x = -7.433034374 Solving -3.5 + x = -7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -7.433034374 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -7.433034374 + 3.5 x = -7.433034374 + 3.5 Combine like terms: -7.433034374 + 3.5 = -3.933034374 x = -3.933034374 Simplifying x = -3.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.933034374, -3.933034374}
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