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Simplifying x2 + -7 = x + 20 Reorder the terms: -7 + x2 = x + 20 Reorder the terms: -7 + x2 = 20 + x Solving -7 + x2 = 20 + x Solving for variable 'x'. Reorder the terms: -7 + -20 + -1x + x2 = 20 + x + -20 + -1x Combine like terms: -7 + -20 = -27 -27 + -1x + x2 = 20 + x + -20 + -1x Reorder the terms: -27 + -1x + x2 = 20 + -20 + x + -1x Combine like terms: 20 + -20 = 0 -27 + -1x + x2 = 0 + x + -1x -27 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -27 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -1x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -1x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -1x + x2 = 0 + 27 -1x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -1x + x2 = 27 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 27 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 27 + 0.25 Combine like terms: 27 + 0.25 = 27.25 0.25 + -1x + x2 = 27.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + -0.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + -0.5 = 5.220153254 Simplifying x + -0.5 = 5.220153254 Reorder the terms: -0.5 + x = 5.220153254 Solving -0.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 5.220153254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.220153254 + 0.5 x = 5.220153254 + 0.5 Combine like terms: 5.220153254 + 0.5 = 5.720153254 x = 5.720153254 Simplifying x = 5.720153254Subproblem 2
x + -0.5 = -5.220153254 Simplifying x + -0.5 = -5.220153254 Reorder the terms: -0.5 + x = -5.220153254 Solving -0.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -5.220153254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.220153254 + 0.5 x = -5.220153254 + 0.5 Combine like terms: -5.220153254 + 0.5 = -4.720153254 x = -4.720153254 Simplifying x = -4.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.720153254, -4.720153254}
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