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Simplifying 3x2 + 14x = 45 Reorder the terms: 14x + 3x2 = 45 Solving 14x + 3x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 14x + 3x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -15 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 4.666666667x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 4.666666667x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4.666666667x + x2 = 0 + 15 4.666666667x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 4.666666667x + x2 = 15 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 = 15 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 15 + 5.444444448 Combine like terms: 15 + 5.444444448 = 20.444444448 5.444444448 + 4.666666667x + x2 = 20.444444448 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 20.444444448 Calculate the square root of the right side: 4.521553322 Break this problem into two subproblems by setting (x + 2.333333334) equal to 4.521553322 and -4.521553322.Subproblem 1
x + 2.333333334 = 4.521553322 Simplifying x + 2.333333334 = 4.521553322 Reorder the terms: 2.333333334 + x = 4.521553322 Solving 2.333333334 + x = 4.521553322 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 = 4.521553322 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 4.521553322 + -2.333333334 x = 4.521553322 + -2.333333334 Combine like terms: 4.521553322 + -2.333333334 = 2.188219988 x = 2.188219988 Simplifying x = 2.188219988Subproblem 2
x + 2.333333334 = -4.521553322 Simplifying x + 2.333333334 = -4.521553322 Reorder the terms: 2.333333334 + x = -4.521553322 Solving 2.333333334 + x = -4.521553322 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 = -4.521553322 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -4.521553322 + -2.333333334 x = -4.521553322 + -2.333333334 Combine like terms: -4.521553322 + -2.333333334 = -6.854886656 x = -6.854886656 Simplifying x = -6.854886656Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.188219988, -6.854886656}
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