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Simplifying x2 + 4x = 145 Reorder the terms: 4x + x2 = 145 Solving 4x + x2 = 145 Solving for variable 'x'. Reorder the terms: -145 + 4x + x2 = 145 + -145 Combine like terms: 145 + -145 = 0 -145 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '145' to each side of the equation. -145 + 4x + 145 + x2 = 0 + 145 Reorder the terms: -145 + 145 + 4x + x2 = 0 + 145 Combine like terms: -145 + 145 = 0 0 + 4x + x2 = 0 + 145 4x + x2 = 0 + 145 Combine like terms: 0 + 145 = 145 4x + x2 = 145 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 145 + 4 Reorder the terms: 4 + 4x + x2 = 145 + 4 Combine like terms: 145 + 4 = 149 4 + 4x + x2 = 149 Factor a perfect square on the left side: (x + 2)(x + 2) = 149 Calculate the square root of the right side: 12.206555616 Break this problem into two subproblems by setting (x + 2) equal to 12.206555616 and -12.206555616.Subproblem 1
x + 2 = 12.206555616 Simplifying x + 2 = 12.206555616 Reorder the terms: 2 + x = 12.206555616 Solving 2 + x = 12.206555616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 12.206555616 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.206555616 + -2 x = 12.206555616 + -2 Combine like terms: 12.206555616 + -2 = 10.206555616 x = 10.206555616 Simplifying x = 10.206555616Subproblem 2
x + 2 = -12.206555616 Simplifying x + 2 = -12.206555616 Reorder the terms: 2 + x = -12.206555616 Solving 2 + x = -12.206555616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -12.206555616 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.206555616 + -2 x = -12.206555616 + -2 Combine like terms: -12.206555616 + -2 = -14.206555616 x = -14.206555616 Simplifying x = -14.206555616Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.206555616, -14.206555616}
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