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Simplifying 3x2 + -52 = 7 + 14x Reorder the terms: -52 + 3x2 = 7 + 14x Solving -52 + 3x2 = 7 + 14x Solving for variable 'x'. Reorder the terms: -52 + -7 + -14x + 3x2 = 7 + 14x + -7 + -14x Combine like terms: -52 + -7 = -59 -59 + -14x + 3x2 = 7 + 14x + -7 + -14x Reorder the terms: -59 + -14x + 3x2 = 7 + -7 + 14x + -14x Combine like terms: 7 + -7 = 0 -59 + -14x + 3x2 = 0 + 14x + -14x -59 + -14x + 3x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -59 + -14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -19.66666667 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '19.66666667' to each side of the equation. -19.66666667 + -4.666666667x + 19.66666667 + x2 = 0 + 19.66666667 Reorder the terms: -19.66666667 + 19.66666667 + -4.666666667x + x2 = 0 + 19.66666667 Combine like terms: -19.66666667 + 19.66666667 = 0.00000000 0.00000000 + -4.666666667x + x2 = 0 + 19.66666667 -4.666666667x + x2 = 0 + 19.66666667 Combine like terms: 0 + 19.66666667 = 19.66666667 -4.666666667x + x2 = 19.66666667 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 19.66666667 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 19.66666667 + 5.444444448 Combine like terms: 19.66666667 + 5.444444448 = 25.111111118 5.444444448 + -4.666666667x + x2 = 25.111111118 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 25.111111118 Calculate the square root of the right side: 5.011098793 Break this problem into two subproblems by setting (x + -2.333333334) equal to 5.011098793 and -5.011098793.Subproblem 1
x + -2.333333334 = 5.011098793 Simplifying x + -2.333333334 = 5.011098793 Reorder the terms: -2.333333334 + x = 5.011098793 Solving -2.333333334 + x = 5.011098793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 5.011098793 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 5.011098793 + 2.333333334 x = 5.011098793 + 2.333333334 Combine like terms: 5.011098793 + 2.333333334 = 7.344432127 x = 7.344432127 Simplifying x = 7.344432127Subproblem 2
x + -2.333333334 = -5.011098793 Simplifying x + -2.333333334 = -5.011098793 Reorder the terms: -2.333333334 + x = -5.011098793 Solving -2.333333334 + x = -5.011098793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -5.011098793 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -5.011098793 + 2.333333334 x = -5.011098793 + 2.333333334 Combine like terms: -5.011098793 + 2.333333334 = -2.677765459 x = -2.677765459 Simplifying x = -2.677765459Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.344432127, -2.677765459}
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