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Simplifying x2 = 10x + 4x + 21 Reorder the terms: x2 = 21 + 10x + 4x Combine like terms: 10x + 4x = 14x x2 = 21 + 14x Solving x2 = 21 + 14x Solving for variable 'x'. Reorder the terms: -21 + -14x + x2 = 21 + 14x + -21 + -14x Reorder the terms: -21 + -14x + x2 = 21 + -21 + 14x + -14x Combine like terms: 21 + -21 = 0 -21 + -14x + x2 = 0 + 14x + -14x -21 + -14x + x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -21 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -14x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -14x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -14x + x2 = 0 + 21 -14x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -14x + x2 = 21 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 = 21 + 49 Reorder the terms: 49 + -14x + x2 = 21 + 49 Combine like terms: 21 + 49 = 70 49 + -14x + x2 = 70 Factor a perfect square on the left side: (x + -7)(x + -7) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (x + -7) equal to 8.366600265 and -8.366600265.Subproblem 1
x + -7 = 8.366600265 Simplifying x + -7 = 8.366600265 Reorder the terms: -7 + x = 8.366600265 Solving -7 + x = 8.366600265 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 = 8.366600265 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.366600265 + 7 x = 8.366600265 + 7 Combine like terms: 8.366600265 + 7 = 15.366600265 x = 15.366600265 Simplifying x = 15.366600265Subproblem 2
x + -7 = -8.366600265 Simplifying x + -7 = -8.366600265 Reorder the terms: -7 + x = -8.366600265 Solving -7 + x = -8.366600265 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 = -8.366600265 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.366600265 + 7 x = -8.366600265 + 7 Combine like terms: -8.366600265 + 7 = -1.366600265 x = -1.366600265 Simplifying x = -1.366600265Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.366600265, -1.366600265}
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