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Simplifying x = x2 + -14x + 39 Reorder the terms: x = 39 + -14x + x2 Solving x = 39 + -14x + x2 Solving for variable 'x'. Reorder the terms: -39 + x + 14x + -1x2 = 39 + -14x + x2 + -39 + 14x + -1x2 Combine like terms: x + 14x = 15x -39 + 15x + -1x2 = 39 + -14x + x2 + -39 + 14x + -1x2 Reorder the terms: -39 + 15x + -1x2 = 39 + -39 + -14x + 14x + x2 + -1x2 Combine like terms: 39 + -39 = 0 -39 + 15x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -39 + 15x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -39 + 15x + -1x2 = 0 + x2 + -1x2 -39 + 15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -39 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 39 + -15x + x2 = 0 Move the constant term to the right: Add '-39' to each side of the equation. 39 + -15x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + -15x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -15x + x2 = 0 + -39 -15x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 -15x + x2 = -39 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 = -39 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -39 + 56.25 Combine like terms: -39 + 56.25 = 17.25 56.25 + -15x + x2 = 17.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + -7.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + -7.5 = 4.153311931 Simplifying x + -7.5 = 4.153311931 Reorder the terms: -7.5 + x = 4.153311931 Solving -7.5 + x = 4.153311931 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 = 4.153311931 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 4.153311931 + 7.5 x = 4.153311931 + 7.5 Combine like terms: 4.153311931 + 7.5 = 11.653311931 x = 11.653311931 Simplifying x = 11.653311931Subproblem 2
x + -7.5 = -4.153311931 Simplifying x + -7.5 = -4.153311931 Reorder the terms: -7.5 + x = -4.153311931 Solving -7.5 + x = -4.153311931 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 = -4.153311931 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -4.153311931 + 7.5 x = -4.153311931 + 7.5 Combine like terms: -4.153311931 + 7.5 = 3.346688069 x = 3.346688069 Simplifying x = 3.346688069Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.653311931, 3.346688069}
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