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Simplifying 3x + 6 = 4x2 + 24x + -124 Reorder the terms: 6 + 3x = 4x2 + 24x + -124 Reorder the terms: 6 + 3x = -124 + 24x + 4x2 Solving 6 + 3x = -124 + 24x + 4x2 Solving for variable 'x'. Reorder the terms: 6 + 124 + 3x + -24x + -4x2 = -124 + 24x + 4x2 + 124 + -24x + -4x2 Combine like terms: 6 + 124 = 130 130 + 3x + -24x + -4x2 = -124 + 24x + 4x2 + 124 + -24x + -4x2 Combine like terms: 3x + -24x = -21x 130 + -21x + -4x2 = -124 + 24x + 4x2 + 124 + -24x + -4x2 Reorder the terms: 130 + -21x + -4x2 = -124 + 124 + 24x + -24x + 4x2 + -4x2 Combine like terms: -124 + 124 = 0 130 + -21x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2 130 + -21x + -4x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 130 + -21x + -4x2 = 0 + 4x2 + -4x2 130 + -21x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 130 + -21x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -32.5 + 5.25x + x2 = 0 Move the constant term to the right: Add '32.5' to each side of the equation. -32.5 + 5.25x + 32.5 + x2 = 0 + 32.5 Reorder the terms: -32.5 + 32.5 + 5.25x + x2 = 0 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + 5.25x + x2 = 0 + 32.5 5.25x + x2 = 0 + 32.5 Combine like terms: 0 + 32.5 = 32.5 5.25x + x2 = 32.5 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = 32.5 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = 32.5 + 6.890625 Combine like terms: 32.5 + 6.890625 = 39.390625 6.890625 + 5.25x + x2 = 39.390625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 39.390625 Calculate the square root of the right side: 6.276195105 Break this problem into two subproblems by setting (x + 2.625) equal to 6.276195105 and -6.276195105.Subproblem 1
x + 2.625 = 6.276195105 Simplifying x + 2.625 = 6.276195105 Reorder the terms: 2.625 + x = 6.276195105 Solving 2.625 + x = 6.276195105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 6.276195105 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 6.276195105 + -2.625 x = 6.276195105 + -2.625 Combine like terms: 6.276195105 + -2.625 = 3.651195105 x = 3.651195105 Simplifying x = 3.651195105Subproblem 2
x + 2.625 = -6.276195105 Simplifying x + 2.625 = -6.276195105 Reorder the terms: 2.625 + x = -6.276195105 Solving 2.625 + x = -6.276195105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -6.276195105 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -6.276195105 + -2.625 x = -6.276195105 + -2.625 Combine like terms: -6.276195105 + -2.625 = -8.901195105 x = -8.901195105 Simplifying x = -8.901195105Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.651195105, -8.901195105}
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