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Simplifying x(2 + 9) * 3x = 8x + 21 Combine like terms: 2 + 9 = 11 x(11) * 3x = 8x + 21 Reorder the terms for easier multiplication: 11 * 3x * x = 8x + 21 Multiply 11 * 3 33x * x = 8x + 21 Multiply x * x 33x2 = 8x + 21 Reorder the terms: 33x2 = 21 + 8x Solving 33x2 = 21 + 8x Solving for variable 'x'. Reorder the terms: -21 + -8x + 33x2 = 21 + 8x + -21 + -8x Reorder the terms: -21 + -8x + 33x2 = 21 + -21 + 8x + -8x Combine like terms: 21 + -21 = 0 -21 + -8x + 33x2 = 0 + 8x + -8x -21 + -8x + 33x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -21 + -8x + 33x2 = 0 Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. -0.6363636364 + -0.2424242424x + x2 = 0 Move the constant term to the right: Add '0.6363636364' to each side of the equation. -0.6363636364 + -0.2424242424x + 0.6363636364 + x2 = 0 + 0.6363636364 Reorder the terms: -0.6363636364 + 0.6363636364 + -0.2424242424x + x2 = 0 + 0.6363636364 Combine like terms: -0.6363636364 + 0.6363636364 = 0.0000000000 0.0000000000 + -0.2424242424x + x2 = 0 + 0.6363636364 -0.2424242424x + x2 = 0 + 0.6363636364 Combine like terms: 0 + 0.6363636364 = 0.6363636364 -0.2424242424x + x2 = 0.6363636364 The x term is -0.2424242424x. Take half its coefficient (-0.1212121212). Square it (0.01469237833) and add it to both sides. Add '0.01469237833' to each side of the equation. -0.2424242424x + 0.01469237833 + x2 = 0.6363636364 + 0.01469237833 Reorder the terms: 0.01469237833 + -0.2424242424x + x2 = 0.6363636364 + 0.01469237833 Combine like terms: 0.6363636364 + 0.01469237833 = 0.65105601473 0.01469237833 + -0.2424242424x + x2 = 0.65105601473 Factor a perfect square on the left side: (x + -0.1212121212)(x + -0.1212121212) = 0.65105601473 Calculate the square root of the right side: 0.806880422 Break this problem into two subproblems by setting (x + -0.1212121212) equal to 0.806880422 and -0.806880422.Subproblem 1
x + -0.1212121212 = 0.806880422 Simplifying x + -0.1212121212 = 0.806880422 Reorder the terms: -0.1212121212 + x = 0.806880422 Solving -0.1212121212 + x = 0.806880422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1212121212' to each side of the equation. -0.1212121212 + 0.1212121212 + x = 0.806880422 + 0.1212121212 Combine like terms: -0.1212121212 + 0.1212121212 = 0.0000000000 0.0000000000 + x = 0.806880422 + 0.1212121212 x = 0.806880422 + 0.1212121212 Combine like terms: 0.806880422 + 0.1212121212 = 0.9280925432 x = 0.9280925432 Simplifying x = 0.9280925432Subproblem 2
x + -0.1212121212 = -0.806880422 Simplifying x + -0.1212121212 = -0.806880422 Reorder the terms: -0.1212121212 + x = -0.806880422 Solving -0.1212121212 + x = -0.806880422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1212121212' to each side of the equation. -0.1212121212 + 0.1212121212 + x = -0.806880422 + 0.1212121212 Combine like terms: -0.1212121212 + 0.1212121212 = 0.0000000000 0.0000000000 + x = -0.806880422 + 0.1212121212 x = -0.806880422 + 0.1212121212 Combine like terms: -0.806880422 + 0.1212121212 = -0.6856683008 x = -0.6856683008 Simplifying x = -0.6856683008Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9280925432, -0.6856683008}
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