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Simplifying x2 + 28x + -4 = 0 Reorder the terms: -4 + 28x + x2 = 0 Solving -4 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 28x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 28x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 28x + x2 = 0 + 4 28x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 28x + x2 = 4 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 4 + 196 Reorder the terms: 196 + 28x + x2 = 4 + 196 Combine like terms: 4 + 196 = 200 196 + 28x + x2 = 200 Factor a perfect square on the left side: (x + 14)(x + 14) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + 14) equal to 14.142135624 and -14.142135624.Subproblem 1
x + 14 = 14.142135624 Simplifying x + 14 = 14.142135624 Reorder the terms: 14 + x = 14.142135624 Solving 14 + x = 14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 14.142135624 + -14 Combine like terms: 14 + -14 = 0 0 + x = 14.142135624 + -14 x = 14.142135624 + -14 Combine like terms: 14.142135624 + -14 = 0.142135624 x = 0.142135624 Simplifying x = 0.142135624Subproblem 2
x + 14 = -14.142135624 Simplifying x + 14 = -14.142135624 Reorder the terms: 14 + x = -14.142135624 Solving 14 + x = -14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -14.142135624 + -14 Combine like terms: 14 + -14 = 0 0 + x = -14.142135624 + -14 x = -14.142135624 + -14 Combine like terms: -14.142135624 + -14 = -28.142135624 x = -28.142135624 Simplifying x = -28.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.142135624, -28.142135624}
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