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Simplifying 16x + 12 + -3x = 7x(3x + -4) Reorder the terms: 12 + 16x + -3x = 7x(3x + -4) Combine like terms: 16x + -3x = 13x 12 + 13x = 7x(3x + -4) Reorder the terms: 12 + 13x = 7x(-4 + 3x) 12 + 13x = (-4 * 7x + 3x * 7x) 12 + 13x = (-28x + 21x2) Solving 12 + 13x = -28x + 21x2 Solving for variable 'x'. Combine like terms: 13x + 28x = 41x 12 + 41x + -21x2 = -28x + 21x2 + 28x + -21x2 Reorder the terms: 12 + 41x + -21x2 = -28x + 28x + 21x2 + -21x2 Combine like terms: -28x + 28x = 0 12 + 41x + -21x2 = 0 + 21x2 + -21x2 12 + 41x + -21x2 = 21x2 + -21x2 Combine like terms: 21x2 + -21x2 = 0 12 + 41x + -21x2 = 0 Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -0.5714285714 + -1.952380952x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -1.952380952x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -1.952380952x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -1.952380952x + x2 = 0 + 0.5714285714 -1.952380952x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -1.952380952x + x2 = 0.5714285714 The x term is -1.952380952x. Take half its coefficient (-0.976190476). Square it (0.9529478454) and add it to both sides. Add '0.9529478454' to each side of the equation. -1.952380952x + 0.9529478454 + x2 = 0.5714285714 + 0.9529478454 Reorder the terms: 0.9529478454 + -1.952380952x + x2 = 0.5714285714 + 0.9529478454 Combine like terms: 0.5714285714 + 0.9529478454 = 1.5243764168 0.9529478454 + -1.952380952x + x2 = 1.5243764168 Factor a perfect square on the left side: (x + -0.976190476)(x + -0.976190476) = 1.5243764168 Calculate the square root of the right side: 1.234656396 Break this problem into two subproblems by setting (x + -0.976190476) equal to 1.234656396 and -1.234656396.Subproblem 1
x + -0.976190476 = 1.234656396 Simplifying x + -0.976190476 = 1.234656396 Reorder the terms: -0.976190476 + x = 1.234656396 Solving -0.976190476 + x = 1.234656396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.976190476' to each side of the equation. -0.976190476 + 0.976190476 + x = 1.234656396 + 0.976190476 Combine like terms: -0.976190476 + 0.976190476 = 0.000000000 0.000000000 + x = 1.234656396 + 0.976190476 x = 1.234656396 + 0.976190476 Combine like terms: 1.234656396 + 0.976190476 = 2.210846872 x = 2.210846872 Simplifying x = 2.210846872Subproblem 2
x + -0.976190476 = -1.234656396 Simplifying x + -0.976190476 = -1.234656396 Reorder the terms: -0.976190476 + x = -1.234656396 Solving -0.976190476 + x = -1.234656396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.976190476' to each side of the equation. -0.976190476 + 0.976190476 + x = -1.234656396 + 0.976190476 Combine like terms: -0.976190476 + 0.976190476 = 0.000000000 0.000000000 + x = -1.234656396 + 0.976190476 x = -1.234656396 + 0.976190476 Combine like terms: -1.234656396 + 0.976190476 = -0.25846592 x = -0.25846592 Simplifying x = -0.25846592Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.210846872, -0.25846592}
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