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Simplifying -3x(5x + 3) = 9x + 2 Reorder the terms: -3x(3 + 5x) = 9x + 2 (3 * -3x + 5x * -3x) = 9x + 2 (-9x + -15x2) = 9x + 2 Reorder the terms: -9x + -15x2 = 2 + 9x Solving -9x + -15x2 = 2 + 9x Solving for variable 'x'. Reorder the terms: -2 + -9x + -9x + -15x2 = 2 + 9x + -2 + -9x Combine like terms: -9x + -9x = -18x -2 + -18x + -15x2 = 2 + 9x + -2 + -9x Reorder the terms: -2 + -18x + -15x2 = 2 + -2 + 9x + -9x Combine like terms: 2 + -2 = 0 -2 + -18x + -15x2 = 0 + 9x + -9x -2 + -18x + -15x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -2 + -18x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 18x + 15x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 18x + 15x2)' equal to zero and attempt to solve: Simplifying 2 + 18x + 15x2 = 0 Solving 2 + 18x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.1333333333 + 1.2x + x2 = 0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + 1.2x + -0.1333333333 + x2 = 0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + 1.2x + x2 = 0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + 1.2x + x2 = 0 + -0.1333333333 1.2x + x2 = 0 + -0.1333333333 Combine like terms: 0 + -0.1333333333 = -0.1333333333 1.2x + x2 = -0.1333333333 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = -0.1333333333 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = -0.1333333333 + 0.36 Combine like terms: -0.1333333333 + 0.36 = 0.2266666667 0.36 + 1.2x + x2 = 0.2266666667 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.2266666667 Calculate the square root of the right side: 0.476095229 Break this problem into two subproblems by setting (x + 0.6) equal to 0.476095229 and -0.476095229.Subproblem 1
x + 0.6 = 0.476095229 Simplifying x + 0.6 = 0.476095229 Reorder the terms: 0.6 + x = 0.476095229 Solving 0.6 + x = 0.476095229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 0.476095229 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.476095229 + -0.6 x = 0.476095229 + -0.6 Combine like terms: 0.476095229 + -0.6 = -0.123904771 x = -0.123904771 Simplifying x = -0.123904771Subproblem 2
x + 0.6 = -0.476095229 Simplifying x + 0.6 = -0.476095229 Reorder the terms: 0.6 + x = -0.476095229 Solving 0.6 + x = -0.476095229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -0.476095229 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.476095229 + -0.6 x = -0.476095229 + -0.6 Combine like terms: -0.476095229 + -0.6 = -1.076095229 x = -1.076095229 Simplifying x = -1.076095229Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.123904771, -1.076095229}Solution
x = {-0.123904771, -1.076095229}
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