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Simplifying x(x + 4) = 159 Reorder the terms: x(4 + x) = 159 (4 * x + x * x) = 159 (4x + x2) = 159 Solving 4x + x2 = 159 Solving for variable 'x'. Reorder the terms: -159 + 4x + x2 = 159 + -159 Combine like terms: 159 + -159 = 0 -159 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '159' to each side of the equation. -159 + 4x + 159 + x2 = 0 + 159 Reorder the terms: -159 + 159 + 4x + x2 = 0 + 159 Combine like terms: -159 + 159 = 0 0 + 4x + x2 = 0 + 159 4x + x2 = 0 + 159 Combine like terms: 0 + 159 = 159 4x + x2 = 159 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 = 159 + 4 Reorder the terms: 4 + 4x + x2 = 159 + 4 Combine like terms: 159 + 4 = 163 4 + 4x + x2 = 163 Factor a perfect square on the left side: (x + 2)(x + 2) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (x + 2) equal to 12.767145335 and -12.767145335.Subproblem 1
x + 2 = 12.767145335 Simplifying x + 2 = 12.767145335 Reorder the terms: 2 + x = 12.767145335 Solving 2 + x = 12.767145335 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 = 12.767145335 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.767145335 + -2 x = 12.767145335 + -2 Combine like terms: 12.767145335 + -2 = 10.767145335 x = 10.767145335 Simplifying x = 10.767145335Subproblem 2
x + 2 = -12.767145335 Simplifying x + 2 = -12.767145335 Reorder the terms: 2 + x = -12.767145335 Solving 2 + x = -12.767145335 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 = -12.767145335 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.767145335 + -2 x = -12.767145335 + -2 Combine like terms: -12.767145335 + -2 = -14.767145335 x = -14.767145335 Simplifying x = -14.767145335Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.767145335, -14.767145335}
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