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Simplifying (x + 4) = x(x + -14) + 5 Reorder the terms: (4 + x) = x(x + -14) + 5 Remove parenthesis around (4 + x) 4 + x = x(x + -14) + 5 Reorder the terms: 4 + x = x(-14 + x) + 5 4 + x = (-14 * x + x * x) + 5 4 + x = (-14x + x2) + 5 Reorder the terms: 4 + x = 5 + -14x + x2 Solving 4 + x = 5 + -14x + x2 Solving for variable 'x'. Reorder the terms: 4 + -5 + x + 14x + -1x2 = 5 + -14x + x2 + -5 + 14x + -1x2 Combine like terms: 4 + -5 = -1 -1 + x + 14x + -1x2 = 5 + -14x + x2 + -5 + 14x + -1x2 Combine like terms: x + 14x = 15x -1 + 15x + -1x2 = 5 + -14x + x2 + -5 + 14x + -1x2 Reorder the terms: -1 + 15x + -1x2 = 5 + -5 + -14x + 14x + x2 + -1x2 Combine like terms: 5 + -5 = 0 -1 + 15x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -1 + 15x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -1 + 15x + -1x2 = 0 + x2 + -1x2 -1 + 15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -15x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -15x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -15x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -15x + x2 = 0 + -1 -15x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -15x + x2 = -1 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -1 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -1 + 56.25 Combine like terms: -1 + 56.25 = 55.25 56.25 + -15x + x2 = 55.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + -7.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + -7.5 = 7.433034374 Simplifying x + -7.5 = 7.433034374 Reorder the terms: -7.5 + x = 7.433034374 Solving -7.5 + x = 7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.433034374 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.433034374 + 7.5 x = 7.433034374 + 7.5 Combine like terms: 7.433034374 + 7.5 = 14.933034374 x = 14.933034374 Simplifying x = 14.933034374Subproblem 2
x + -7.5 = -7.433034374 Simplifying x + -7.5 = -7.433034374 Reorder the terms: -7.5 + x = -7.433034374 Solving -7.5 + x = -7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.433034374 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.433034374 + 7.5 x = -7.433034374 + 7.5 Combine like terms: -7.433034374 + 7.5 = 0.066965626 x = 0.066965626 Simplifying x = 0.066965626Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.933034374, 0.066965626}
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