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Simplifying 5x(3x + 2) = 9 Reorder the terms: 5x(2 + 3x) = 9 (2 * 5x + 3x * 5x) = 9 (10x + 15x2) = 9 Solving 10x + 15x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 10x + 15x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 10x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.6 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 0.6666666667x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 0.6666666667x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 0.6666666667x + x2 = 0 + 0.6 0.6666666667x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 0.6666666667x + x2 = 0.6 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 = 0.6 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.6 + 0.1111111112 Combine like terms: 0.6 + 0.1111111112 = 0.7111111112 0.1111111112 + 0.6666666667x + x2 = 0.7111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.7111111112 Calculate the square root of the right side: 0.843274043 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.843274043 and -0.843274043.Subproblem 1
x + 0.3333333334 = 0.843274043 Simplifying x + 0.3333333334 = 0.843274043 Reorder the terms: 0.3333333334 + x = 0.843274043 Solving 0.3333333334 + x = 0.843274043 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 = 0.843274043 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.843274043 + -0.3333333334 x = 0.843274043 + -0.3333333334 Combine like terms: 0.843274043 + -0.3333333334 = 0.5099407096 x = 0.5099407096 Simplifying x = 0.5099407096Subproblem 2
x + 0.3333333334 = -0.843274043 Simplifying x + 0.3333333334 = -0.843274043 Reorder the terms: 0.3333333334 + x = -0.843274043 Solving 0.3333333334 + x = -0.843274043 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 = -0.843274043 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.843274043 + -0.3333333334 x = -0.843274043 + -0.3333333334 Combine like terms: -0.843274043 + -0.3333333334 = -1.1766073764 x = -1.1766073764 Simplifying x = -1.1766073764Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5099407096, -1.1766073764}
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