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Simplifying x2 + -20x + 7 = 7x + -5 Reorder the terms: 7 + -20x + x2 = 7x + -5 Reorder the terms: 7 + -20x + x2 = -5 + 7x Solving 7 + -20x + x2 = -5 + 7x Solving for variable 'x'. Reorder the terms: 7 + 5 + -20x + -7x + x2 = -5 + 7x + 5 + -7x Combine like terms: 7 + 5 = 12 12 + -20x + -7x + x2 = -5 + 7x + 5 + -7x Combine like terms: -20x + -7x = -27x 12 + -27x + x2 = -5 + 7x + 5 + -7x Reorder the terms: 12 + -27x + x2 = -5 + 5 + 7x + -7x Combine like terms: -5 + 5 = 0 12 + -27x + x2 = 0 + 7x + -7x 12 + -27x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 12 + -27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -27x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -27x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -27x + x2 = 0 + -12 -27x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -27x + x2 = -12 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = -12 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -12 + 182.25 Combine like terms: -12 + 182.25 = 170.25 182.25 + -27x + x2 = 170.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 170.25 Calculate the square root of the right side: 13.047988351 Break this problem into two subproblems by setting (x + -13.5) equal to 13.047988351 and -13.047988351.Subproblem 1
x + -13.5 = 13.047988351 Simplifying x + -13.5 = 13.047988351 Reorder the terms: -13.5 + x = 13.047988351 Solving -13.5 + x = 13.047988351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 13.047988351 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 13.047988351 + 13.5 x = 13.047988351 + 13.5 Combine like terms: 13.047988351 + 13.5 = 26.547988351 x = 26.547988351 Simplifying x = 26.547988351Subproblem 2
x + -13.5 = -13.047988351 Simplifying x + -13.5 = -13.047988351 Reorder the terms: -13.5 + x = -13.047988351 Solving -13.5 + x = -13.047988351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -13.047988351 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -13.047988351 + 13.5 x = -13.047988351 + 13.5 Combine like terms: -13.047988351 + 13.5 = 0.452011649 x = 0.452011649 Simplifying x = 0.452011649Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.547988351, 0.452011649}
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