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Simplifying 3x2 + -42x = -14 Reorder the terms: -42x + 3x2 = -14 Solving -42x + 3x2 = -14 Solving for variable 'x'. Reorder the terms: 14 + -42x + 3x2 = -14 + 14 Combine like terms: -14 + 14 = 0 14 + -42x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.666666667 + -14x + x2 = 0 Move the constant term to the right: Add '-4.666666667' to each side of the equation. 4.666666667 + -14x + -4.666666667 + x2 = 0 + -4.666666667 Reorder the terms: 4.666666667 + -4.666666667 + -14x + x2 = 0 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + -14x + x2 = 0 + -4.666666667 -14x + x2 = 0 + -4.666666667 Combine like terms: 0 + -4.666666667 = -4.666666667 -14x + x2 = -4.666666667 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 = -4.666666667 + 49 Reorder the terms: 49 + -14x + x2 = -4.666666667 + 49 Combine like terms: -4.666666667 + 49 = 44.333333333 49 + -14x + x2 = 44.333333333 Factor a perfect square on the left side: (x + -7)(x + -7) = 44.333333333 Calculate the square root of the right side: 6.658328118 Break this problem into two subproblems by setting (x + -7) equal to 6.658328118 and -6.658328118.Subproblem 1
x + -7 = 6.658328118 Simplifying x + -7 = 6.658328118 Reorder the terms: -7 + x = 6.658328118 Solving -7 + x = 6.658328118 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 = 6.658328118 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.658328118 + 7 x = 6.658328118 + 7 Combine like terms: 6.658328118 + 7 = 13.658328118 x = 13.658328118 Simplifying x = 13.658328118Subproblem 2
x + -7 = -6.658328118 Simplifying x + -7 = -6.658328118 Reorder the terms: -7 + x = -6.658328118 Solving -7 + x = -6.658328118 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 = -6.658328118 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.658328118 + 7 x = -6.658328118 + 7 Combine like terms: -6.658328118 + 7 = 0.341671882 x = 0.341671882 Simplifying x = 0.341671882Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.658328118, 0.341671882}
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