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Simplifying 3x2 + 7x + -7 = 14 Reorder the terms: -7 + 7x + 3x2 = 14 Solving -7 + 7x + 3x2 = 14 Solving for variable 'x'. Reorder the terms: -7 + -14 + 7x + 3x2 = 14 + -14 Combine like terms: -7 + -14 = -21 -21 + 7x + 3x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -21 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 2.333333333x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 2.333333333x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2.333333333x + x2 = 0 + 7 2.333333333x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 2.333333333x + x2 = 7 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 7 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 7 + 1.361111112 Combine like terms: 7 + 1.361111112 = 8.361111112 1.361111112 + 2.333333333x + x2 = 8.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 8.361111112 Calculate the square root of the right side: 2.891558596 Break this problem into two subproblems by setting (x + 1.166666667) equal to 2.891558596 and -2.891558596.Subproblem 1
x + 1.166666667 = 2.891558596 Simplifying x + 1.166666667 = 2.891558596 Reorder the terms: 1.166666667 + x = 2.891558596 Solving 1.166666667 + x = 2.891558596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 2.891558596 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 2.891558596 + -1.166666667 x = 2.891558596 + -1.166666667 Combine like terms: 2.891558596 + -1.166666667 = 1.724891929 x = 1.724891929 Simplifying x = 1.724891929Subproblem 2
x + 1.166666667 = -2.891558596 Simplifying x + 1.166666667 = -2.891558596 Reorder the terms: 1.166666667 + x = -2.891558596 Solving 1.166666667 + x = -2.891558596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -2.891558596 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -2.891558596 + -1.166666667 x = -2.891558596 + -1.166666667 Combine like terms: -2.891558596 + -1.166666667 = -4.058225263 x = -4.058225263 Simplifying x = -4.058225263Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.724891929, -4.058225263}
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