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Simplifying 0 = 3x2 + -42x + 110 Reorder the terms: 0 = 110 + -42x + 3x2 Solving 0 = 110 + -42x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -110 = -110 -110 + 42x + -3x2 = 110 + -42x + 3x2 + -110 + 42x + -3x2 Reorder the terms: -110 + 42x + -3x2 = 110 + -110 + -42x + 42x + 3x2 + -3x2 Combine like terms: 110 + -110 = 0 -110 + 42x + -3x2 = 0 + -42x + 42x + 3x2 + -3x2 -110 + 42x + -3x2 = -42x + 42x + 3x2 + -3x2 Combine like terms: -42x + 42x = 0 -110 + 42x + -3x2 = 0 + 3x2 + -3x2 -110 + 42x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -110 + 42x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 36.66666667 + -14x + x2 = 0 Move the constant term to the right: Add '-36.66666667' to each side of the equation. 36.66666667 + -14x + -36.66666667 + x2 = 0 + -36.66666667 Reorder the terms: 36.66666667 + -36.66666667 + -14x + x2 = 0 + -36.66666667 Combine like terms: 36.66666667 + -36.66666667 = 0.00000000 0.00000000 + -14x + x2 = 0 + -36.66666667 -14x + x2 = 0 + -36.66666667 Combine like terms: 0 + -36.66666667 = -36.66666667 -14x + x2 = -36.66666667 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 = -36.66666667 + 49 Reorder the terms: 49 + -14x + x2 = -36.66666667 + 49 Combine like terms: -36.66666667 + 49 = 12.33333333 49 + -14x + x2 = 12.33333333 Factor a perfect square on the left side: (x + -7)(x + -7) = 12.33333333 Calculate the square root of the right side: 3.511884584 Break this problem into two subproblems by setting (x + -7) equal to 3.511884584 and -3.511884584.Subproblem 1
x + -7 = 3.511884584 Simplifying x + -7 = 3.511884584 Reorder the terms: -7 + x = 3.511884584 Solving -7 + x = 3.511884584 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 = 3.511884584 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3.511884584 + 7 x = 3.511884584 + 7 Combine like terms: 3.511884584 + 7 = 10.511884584 x = 10.511884584 Simplifying x = 10.511884584Subproblem 2
x + -7 = -3.511884584 Simplifying x + -7 = -3.511884584 Reorder the terms: -7 + x = -3.511884584 Solving -7 + x = -3.511884584 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 = -3.511884584 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3.511884584 + 7 x = -3.511884584 + 7 Combine like terms: -3.511884584 + 7 = 3.488115416 x = 3.488115416 Simplifying x = 3.488115416Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.511884584, 3.488115416}
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