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Simplifying 144 = x2 + 4x Reorder the terms: 144 = 4x + x2 Solving 144 = 4x + x2 Solving for variable 'x'. Reorder the terms: 144 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 144 + -4x + -1x2 = 0 + x2 + -1x2 144 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 144 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -144 + 4x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + 4x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 4x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 4x + x2 = 0 + 144 4x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 4x + x2 = 144 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 = 144 + 4 Reorder the terms: 4 + 4x + x2 = 144 + 4 Combine like terms: 144 + 4 = 148 4 + 4x + x2 = 148 Factor a perfect square on the left side: (x + 2)(x + 2) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (x + 2) equal to 12.165525061 and -12.165525061.Subproblem 1
x + 2 = 12.165525061 Simplifying x + 2 = 12.165525061 Reorder the terms: 2 + x = 12.165525061 Solving 2 + x = 12.165525061 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 = 12.165525061 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.165525061 + -2 x = 12.165525061 + -2 Combine like terms: 12.165525061 + -2 = 10.165525061 x = 10.165525061 Simplifying x = 10.165525061Subproblem 2
x + 2 = -12.165525061 Simplifying x + 2 = -12.165525061 Reorder the terms: 2 + x = -12.165525061 Solving 2 + x = -12.165525061 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 = -12.165525061 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.165525061 + -2 x = -12.165525061 + -2 Combine like terms: -12.165525061 + -2 = -14.165525061 x = -14.165525061 Simplifying x = -14.165525061Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.165525061, -14.165525061}
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