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Simplifying 4x(x + -3) + -2 = 92 Reorder the terms: 4x(-3 + x) + -2 = 92 (-3 * 4x + x * 4x) + -2 = 92 (-12x + 4x2) + -2 = 92 Reorder the terms: -2 + -12x + 4x2 = 92 Solving -2 + -12x + 4x2 = 92 Solving for variable 'x'. Reorder the terms: -2 + -92 + -12x + 4x2 = 92 + -92 Combine like terms: -2 + -92 = -94 -94 + -12x + 4x2 = 92 + -92 Combine like terms: 92 + -92 = 0 -94 + -12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + -6x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + -6x + 2x2)' equal to zero and attempt to solve: Simplifying -47 + -6x + 2x2 = 0 Solving -47 + -6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23.5 + -3x + x2 = 0 Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + -3x + 23.5 + x2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + -3x + x2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + -3x + x2 = 0 + 23.5 -3x + x2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 -3x + x2 = 23.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 23.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 23.5 + 2.25 Combine like terms: 23.5 + 2.25 = 25.75 2.25 + -3x + x2 = 25.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 25.75 Calculate the square root of the right side: 5.074445783 Break this problem into two subproblems by setting (x + -1.5) equal to 5.074445783 and -5.074445783.Subproblem 1
x + -1.5 = 5.074445783 Simplifying x + -1.5 = 5.074445783 Reorder the terms: -1.5 + x = 5.074445783 Solving -1.5 + x = 5.074445783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 5.074445783 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.074445783 + 1.5 x = 5.074445783 + 1.5 Combine like terms: 5.074445783 + 1.5 = 6.574445783 x = 6.574445783 Simplifying x = 6.574445783Subproblem 2
x + -1.5 = -5.074445783 Simplifying x + -1.5 = -5.074445783 Reorder the terms: -1.5 + x = -5.074445783 Solving -1.5 + x = -5.074445783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -5.074445783 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.074445783 + 1.5 x = -5.074445783 + 1.5 Combine like terms: -5.074445783 + 1.5 = -3.574445783 x = -3.574445783 Simplifying x = -3.574445783Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.574445783, -3.574445783}Solution
x = {6.574445783, -3.574445783}
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