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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 = 53.666666667 49 + -14x + x2 = 53.666666667 Factor a perfect square on the left side: (x + -7)(x + -7) = 53.666666667 Calculate the square root of the right side: 7.325753659 Break this problem into two subproblems by setting (x + -7) equal to 7.325753659 and -7.325753659.Subproblem 1
x + -7 = 7.325753659 Simplifying x + -7 = 7.325753659 Reorder the terms: -7 + x = 7.325753659 Solving -7 + x = 7.325753659 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 = 7.325753659 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.325753659 + 7 x = 7.325753659 + 7 Combine like terms: 7.325753659 + 7 = 14.325753659 x = 14.325753659 Simplifying x = 14.325753659Subproblem 2
x + -7 = -7.325753659 Simplifying x + -7 = -7.325753659 Reorder the terms: -7 + x = -7.325753659 Solving -7 + x = -7.325753659 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 = -7.325753659 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.325753659 + 7 x = -7.325753659 + 7 Combine like terms: -7.325753659 + 7 = -0.325753659 x = -0.325753659 Simplifying x = -0.325753659Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.325753659, -0.325753659}
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