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Simplifying 14x + -16 = x2 Reorder the terms: -16 + 14x = x2 Solving -16 + 14x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 -16 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 16 + -14x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -14x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -14x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -14x + x2 = 0 + -16 -14x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -14x + x2 = -16 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -16 + 49 Reorder the terms: 49 + -14x + x2 = -16 + 49 Combine like terms: -16 + 49 = 33 49 + -14x + x2 = 33 Factor a perfect square on the left side: (x + -7)(x + -7) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + -7) equal to 5.744562647 and -5.744562647.Subproblem 1
x + -7 = 5.744562647 Simplifying x + -7 = 5.744562647 Reorder the terms: -7 + x = 5.744562647 Solving -7 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 5.744562647 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.744562647 + 7 x = 5.744562647 + 7 Combine like terms: 5.744562647 + 7 = 12.744562647 x = 12.744562647 Simplifying x = 12.744562647Subproblem 2
x + -7 = -5.744562647 Simplifying x + -7 = -5.744562647 Reorder the terms: -7 + x = -5.744562647 Solving -7 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -5.744562647 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.744562647 + 7 x = -5.744562647 + 7 Combine like terms: -5.744562647 + 7 = 1.255437353 x = 1.255437353 Simplifying x = 1.255437353Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.744562647, 1.255437353}
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