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Simplifying 4x(x) + -2(24) * x + 3(24) + -5 = 0 Multiply x * x 4x2 + -2(24) * x + 3(24) + -5 = 0 Multiply -2 * 24 4x2 + -48x + 3(24) + -5 = 0 Multiply 3 * 24 4x2 + -48x + 72 + -5 = 0 Reorder the terms: 72 + -5 + -48x + 4x2 = 0 Combine like terms: 72 + -5 = 67 67 + -48x + 4x2 = 0 Solving 67 + -48x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 16.75 + -12x + x2 = 0 Move the constant term to the right: Add '-16.75' to each side of the equation. 16.75 + -12x + -16.75 + x2 = 0 + -16.75 Reorder the terms: 16.75 + -16.75 + -12x + x2 = 0 + -16.75 Combine like terms: 16.75 + -16.75 = 0.00 0.00 + -12x + x2 = 0 + -16.75 -12x + x2 = 0 + -16.75 Combine like terms: 0 + -16.75 = -16.75 -12x + x2 = -16.75 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -16.75 + 36 Reorder the terms: 36 + -12x + x2 = -16.75 + 36 Combine like terms: -16.75 + 36 = 19.25 36 + -12x + x2 = 19.25 Factor a perfect square on the left side: (x + -6)(x + -6) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + -6) equal to 4.387482194 and -4.387482194.Subproblem 1
x + -6 = 4.387482194 Simplifying x + -6 = 4.387482194 Reorder the terms: -6 + x = 4.387482194 Solving -6 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.387482194 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.387482194 + 6 x = 4.387482194 + 6 Combine like terms: 4.387482194 + 6 = 10.387482194 x = 10.387482194 Simplifying x = 10.387482194Subproblem 2
x + -6 = -4.387482194 Simplifying x + -6 = -4.387482194 Reorder the terms: -6 + x = -4.387482194 Solving -6 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.387482194 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.387482194 + 6 x = -4.387482194 + 6 Combine like terms: -4.387482194 + 6 = 1.612517806 x = 1.612517806 Simplifying x = 1.612517806Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.387482194, 1.612517806}
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