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Simplifying 3x2 + 2x = 150 Reorder the terms: 2x + 3x2 = 150 Solving 2x + 3x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 2x + 3x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -50 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 0.6666666667x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 0.6666666667x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 0.6666666667x + x2 = 0 + 50 0.6666666667x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 0.6666666667x + x2 = 50 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 = 50 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 50 + 0.1111111112 Combine like terms: 50 + 0.1111111112 = 50.1111111112 0.1111111112 + 0.6666666667x + x2 = 50.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 50.1111111112 Calculate the square root of the right side: 7.078920194 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 7.078920194 and -7.078920194.Subproblem 1
x + 0.3333333334 = 7.078920194 Simplifying x + 0.3333333334 = 7.078920194 Reorder the terms: 0.3333333334 + x = 7.078920194 Solving 0.3333333334 + x = 7.078920194 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 = 7.078920194 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 7.078920194 + -0.3333333334 x = 7.078920194 + -0.3333333334 Combine like terms: 7.078920194 + -0.3333333334 = 6.7455868606 x = 6.7455868606 Simplifying x = 6.7455868606Subproblem 2
x + 0.3333333334 = -7.078920194 Simplifying x + 0.3333333334 = -7.078920194 Reorder the terms: 0.3333333334 + x = -7.078920194 Solving 0.3333333334 + x = -7.078920194 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 = -7.078920194 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -7.078920194 + -0.3333333334 x = -7.078920194 + -0.3333333334 Combine like terms: -7.078920194 + -0.3333333334 = -7.4122535274 x = -7.4122535274 Simplifying x = -7.4122535274Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.7455868606, -7.4122535274}
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