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Simplifying 12x * x + 8x = 189 Multiply x * x 12x2 + 8x = 189 Reorder the terms: 8x + 12x2 = 189 Solving 8x + 12x2 = 189 Solving for variable 'x'. Reorder the terms: -189 + 8x + 12x2 = 189 + -189 Combine like terms: 189 + -189 = 0 -189 + 8x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -15.75 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '15.75' to each side of the equation. -15.75 + 0.6666666667x + 15.75 + x2 = 0 + 15.75 Reorder the terms: -15.75 + 15.75 + 0.6666666667x + x2 = 0 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + 0.6666666667x + x2 = 0 + 15.75 0.6666666667x + x2 = 0 + 15.75 Combine like terms: 0 + 15.75 = 15.75 0.6666666667x + x2 = 15.75 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 = 15.75 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 15.75 + 0.1111111112 Combine like terms: 15.75 + 0.1111111112 = 15.8611111112 0.1111111112 + 0.6666666667x + x2 = 15.8611111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 15.8611111112 Calculate the square root of the right side: 3.982601048 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 3.982601048 and -3.982601048.Subproblem 1
x + 0.3333333334 = 3.982601048 Simplifying x + 0.3333333334 = 3.982601048 Reorder the terms: 0.3333333334 + x = 3.982601048 Solving 0.3333333334 + x = 3.982601048 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 = 3.982601048 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 3.982601048 + -0.3333333334 x = 3.982601048 + -0.3333333334 Combine like terms: 3.982601048 + -0.3333333334 = 3.6492677146 x = 3.6492677146 Simplifying x = 3.6492677146Subproblem 2
x + 0.3333333334 = -3.982601048 Simplifying x + 0.3333333334 = -3.982601048 Reorder the terms: 0.3333333334 + x = -3.982601048 Solving 0.3333333334 + x = -3.982601048 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 = -3.982601048 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -3.982601048 + -0.3333333334 x = -3.982601048 + -0.3333333334 Combine like terms: -3.982601048 + -0.3333333334 = -4.3159343814 x = -4.3159343814 Simplifying x = -4.3159343814Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6492677146, -4.3159343814}
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