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Simplifying x2 + -9x + 20 = 5x + 45 Reorder the terms: 20 + -9x + x2 = 5x + 45 Reorder the terms: 20 + -9x + x2 = 45 + 5x Solving 20 + -9x + x2 = 45 + 5x Solving for variable 'x'. Reorder the terms: 20 + -45 + -9x + -5x + x2 = 45 + 5x + -45 + -5x Combine like terms: 20 + -45 = -25 -25 + -9x + -5x + x2 = 45 + 5x + -45 + -5x Combine like terms: -9x + -5x = -14x -25 + -14x + x2 = 45 + 5x + -45 + -5x Reorder the terms: -25 + -14x + x2 = 45 + -45 + 5x + -5x Combine like terms: 45 + -45 = 0 -25 + -14x + x2 = 0 + 5x + -5x -25 + -14x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -25 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -14x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -14x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -14x + x2 = 0 + 25 -14x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -14x + x2 = 25 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 = 25 + 49 Reorder the terms: 49 + -14x + x2 = 25 + 49 Combine like terms: 25 + 49 = 74 49 + -14x + x2 = 74 Factor a perfect square on the left side: (x + -7)(x + -7) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (x + -7) equal to 8.602325267 and -8.602325267.Subproblem 1
x + -7 = 8.602325267 Simplifying x + -7 = 8.602325267 Reorder the terms: -7 + x = 8.602325267 Solving -7 + x = 8.602325267 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 = 8.602325267 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.602325267 + 7 x = 8.602325267 + 7 Combine like terms: 8.602325267 + 7 = 15.602325267 x = 15.602325267 Simplifying x = 15.602325267Subproblem 2
x + -7 = -8.602325267 Simplifying x + -7 = -8.602325267 Reorder the terms: -7 + x = -8.602325267 Solving -7 + x = -8.602325267 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 = -8.602325267 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.602325267 + 7 x = -8.602325267 + 7 Combine like terms: -8.602325267 + 7 = -1.602325267 x = -1.602325267 Simplifying x = -1.602325267Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.602325267, -1.602325267}
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