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Simplifying 0 = x2 + 4x + -14.153 Reorder the terms: 0 = -14.153 + 4x + x2 Solving 0 = -14.153 + 4x + x2 Solving for variable 'x'. Combine like terms: 0 + 14.153 = 14.153 14.153 + -4x + -1x2 = -14.153 + 4x + x2 + 14.153 + -4x + -1x2 Reorder the terms: 14.153 + -4x + -1x2 = -14.153 + 14.153 + 4x + -4x + x2 + -1x2 Combine like terms: -14.153 + 14.153 = 0.000 14.153 + -4x + -1x2 = 0.000 + 4x + -4x + x2 + -1x2 14.153 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 14.153 + -4x + -1x2 = 0 + x2 + -1x2 14.153 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 14.153 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14.153 + 4x + x2 = 0 Move the constant term to the right: Add '14.153' to each side of the equation. -14.153 + 4x + 14.153 + x2 = 0 + 14.153 Reorder the terms: -14.153 + 14.153 + 4x + x2 = 0 + 14.153 Combine like terms: -14.153 + 14.153 = 0.000 0.000 + 4x + x2 = 0 + 14.153 4x + x2 = 0 + 14.153 Combine like terms: 0 + 14.153 = 14.153 4x + x2 = 14.153 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 = 14.153 + 4 Reorder the terms: 4 + 4x + x2 = 14.153 + 4 Combine like terms: 14.153 + 4 = 18.153 4 + 4x + x2 = 18.153 Factor a perfect square on the left side: (x + 2)(x + 2) = 18.153 Calculate the square root of the right side: 4.260633756 Break this problem into two subproblems by setting (x + 2) equal to 4.260633756 and -4.260633756.Subproblem 1
x + 2 = 4.260633756 Simplifying x + 2 = 4.260633756 Reorder the terms: 2 + x = 4.260633756 Solving 2 + x = 4.260633756 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 = 4.260633756 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.260633756 + -2 x = 4.260633756 + -2 Combine like terms: 4.260633756 + -2 = 2.260633756 x = 2.260633756 Simplifying x = 2.260633756Subproblem 2
x + 2 = -4.260633756 Simplifying x + 2 = -4.260633756 Reorder the terms: 2 + x = -4.260633756 Solving 2 + x = -4.260633756 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 = -4.260633756 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.260633756 + -2 x = -4.260633756 + -2 Combine like terms: -4.260633756 + -2 = -6.260633756 x = -6.260633756 Simplifying x = -6.260633756Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.260633756, -6.260633756}
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