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Simplifying 3x2 + 2x = 75 Reorder the terms: 2x + 3x2 = 75 Solving 2x + 3x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 2x + 3x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -25 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 0.6666666667x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 0.6666666667x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 0.6666666667x + x2 = 0 + 25 0.6666666667x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 0.6666666667x + x2 = 25 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 25 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 25 + 0.1111111112 Combine like terms: 25 + 0.1111111112 = 25.1111111112 0.1111111112 + 0.6666666667x + x2 = 25.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 25.1111111112 Calculate the square root of the right side: 5.011098793 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 5.011098793 and -5.011098793.Subproblem 1
x + 0.3333333334 = 5.011098793 Simplifying x + 0.3333333334 = 5.011098793 Reorder the terms: 0.3333333334 + x = 5.011098793 Solving 0.3333333334 + x = 5.011098793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 5.011098793 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 5.011098793 + -0.3333333334 x = 5.011098793 + -0.3333333334 Combine like terms: 5.011098793 + -0.3333333334 = 4.6777654596 x = 4.6777654596 Simplifying x = 4.6777654596Subproblem 2
x + 0.3333333334 = -5.011098793 Simplifying x + 0.3333333334 = -5.011098793 Reorder the terms: 0.3333333334 + x = -5.011098793 Solving 0.3333333334 + x = -5.011098793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -5.011098793 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -5.011098793 + -0.3333333334 x = -5.011098793 + -0.3333333334 Combine like terms: -5.011098793 + -0.3333333334 = -5.3444321264 x = -5.3444321264 Simplifying x = -5.3444321264Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.6777654596, -5.3444321264}
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